How many possible outcomes are there for the experiment of choosing rock paper or scissors at random?

Breaking it down, there are a total of nine possible matchups, giving each outcome a probability of 1/9. Three of these outcomes are ties, giving a probability of 1/3. This leaves 6/9 probability that choice1 and choice2 are different.

Now 3/6 are choice1 and 3/6 are choice2. Notice how the probability that either will win is 1/2? This suggests a very simple nested if structure. The fact that we return for both true and false conditions in the nested if’s rules out the need for else if.

// first we rule out a tie
// since we return, code below is not executed
// for simplicity, choice1 is a; choice2 is b
if (a===b) {
    return "Tied!";
}
// now we're down to 6 out of 9
// split down the middle gives us 3 outer if's
if (a==="rock") {
    // b can only be scissors or paper
}
if (a==="paper") {
    // b can only be rock or scissors
}
if (a==="scissors") {
    // b can only be paper or rock
}

So now we see that the inner if’s will be if-else‘s:

if (b==="scissors") {
    return "rock wins";
} else {
    return "paper wins";
}

I’ll leave you put it all together. Just insert this if pattern into the above three if’s. Edit as needed in each case, using text and variable names given in the lesson.

Example 1

Determine the sample space for the following experiment:

Choosing one of the four possible aces from a standard deck of cards.

Example 2

Determine the sample space for the following experiment:

Choosing a club from a standard deck of cards.

Example 3

Determine the sample space for the following experiment:

Flipping two coins at the same time.

Example 4

Write the set for the following event:

Rolling an odd number on a standard 6-sided die.

Example 5

Write the set for the following event:

Getting heads on a coin flip.

Example 6

Write the set for the following event:

Getting exactly one head after flipping two coins.

Example 7

How many possible outcomes are there for the experiment of choosing rock, paper, or scissors at random?

Example 8

How many possible outcomes are there for the experiment of choosing a color of the rainbow at random? What is the sample space? 

Example 9

What is the probability of rolling a 5 with a fair die?

Example 10

What is the probability of rolling either 1 or 2 with a fair die?

Example 11

What is the probability of drawing the ace of spades at random from a deck of cards (no jokers)? The one in your sleeve doesn't count.

Example 12

What is the probability of drawing a king at random from a deck of cards (no jokers)? The one in your right pant leg doesn't count.

Example 13

What is the probability of drawing a king at random from a deck of cards (with 2 jokers included)?

Example 14

What is the probability of landing at least one tail with two fair coin flips?

Example 15

What is the probability of landing exactly two heads with three fair coin flips?

Source: Huntstock.com/Shutterstock

“No washing dishes for me tonight," I said after I beat my sister at a game of Rock-Paper-Scissors (RPS). I was 10, and RPS was our “go-to” game of fate to decide all kinds of issues. Little did I know that RPS was not a game of chance, but a strategic system with a strong psychological foundation.

RPS probably dates back to the Han Dynasty in China (206 BC – 220AD). The game, known as “sansukumi-ken” in Japan (hand, three-way, deadlock), has used fingers and hands to represent a variety of different symbols in addition to rock, paper, and scissors, including slugs, poisonous centipedes, frogs, and hunters. By the 20th century, RPS had spread to the West. English names such as roshambo, ick-ack-ock, ching-chang-walla, or stone-paper-scissors have also been used.

RPS is technically a zero-sum hand game (meaning one person’s loss is exactly equal to another person’s gain) played between two people in which each player simultaneously creates one of three shapes with their hand. The shapes are “rock” (a fist), “paper” (a flat hand), and “scissors” (a fist with the index and middle fingers forming a V).

Source: Neil Farber

There are four possible outcomes: 1) tie; 2) rock crushes scissors; 3) paper covers rock; 4) scissors cut paper. (For those looking for an in-depth discussion of RPS, check out The Official Rock Paper Scissors Strategy Guide by Douglas Walker and Graham Walker. Several of the strategies are based on this book and those found at the World RPS Society Website—yes, there is a World RPS Society.)

Many people (including me) may have thought that RPS was similar to flipping coins or throwing dice—a useful method to choose something at random. However, there’s far more to the game than meets the eye. RPS involves observation, mindfulness, manipulation, emotional intelligence, strategy, and skill. And some of that skill involves exploiting your opponent’s non-random behavior.

If people were truly playing RPS in random fashion, it would be impossible to employ any strategy. You would do best to just choose your weapon at random. Eventually, you would have an equal likelihood of winning, losing, or tying. Several small-scale experiments have confirmed this strategy—where every player chooses the three actions with equal probability in each round—often seems to be in effect.

Source: Neil Farber

Then a study out of China by Zhijian Wang at Zhejiang University suggested that RPS is actually a game of psychology more than chance, thus making it possible to exploit your opponent’s predictable patterns.

Zhijian and colleagues looked at 360 students divided into 60 groups. In each group, the players played 300 rounds of RPS against each other. The winners were paid in proportion to the number of their victories.

On the surface, the results of the study appeared to be no surprise: The players in all the groups chose each action about one-third of the time—just as if it was random. But taking a closer look at their behavior uncovers a strategy called “conditional response,” or what turns out to be a “win-stay, lose-shift” strategy.

These findings inspire further questions as to whether this conditional response is a hard-wired neural mechanism or a learned process intrinsic in basic decision-making. When players try to employ some kind of strategy, they decrease the chances that the game will remain random.

Source: Neil Farber

Here are psychological strategies employed by RPS aficionados to use against non-random opponents.

1. Expect repetition. Winners tend to stick with the same action that led to their success. We repeat what works. So, if you lose with rock (they played paper), they’ll play with paper again next and you should go with scissors. In other words, when you lose, jump ahead two actions in the sequence.
2. Follow the sequence when your opponent loses. Losers change their strategy and move to the next action (clockwise: R – P – S) in the sequence. If they lose with rock (you played paper), they’ll play paper next. So you should play scissors. In other words, when you win, go to the next action in the sequence.
3. Know the symbols. There may be subliminal reasons for your opponent choosing a particular symbol. Rock: Very aggressive, symbolized by the fist. Players subconsciously think of rock as a weapon and will rely on it when other strategies are not working. Scissors: Some aggression, as they are sharp and dangerous, but also useful craft tools. Represent controlled aggression used as a clever throw—often when someone is confident or winning. Paper: The most subtle move. An open hand is passive, peaceful, and friendly. Some players won’t use this when falling behind because it may symbolize weakness. Other players identify paper with writing and as such, the power of print is a subtle attack. In those cases, paper may be used to signify superiority.
4. Choose rock for rookies. Rock is a typical opening move for rookies, especially for men, since rock is associated with strength and fortitude. Knowing this, a good opening move against a novice is often paper.
5. Think ahead, like in a chess match. Against a more seasoned opponent, they will purposefully not begin with rock, which is too obvious. They may consider you to be a novice, expect rock and will therefore open with paper. Against a veteran, you should lead with scissors: at worst, you’ll tie.
6. Manipulate your opponent. Gently manipulate your opponent toward choosing a particular action, or not choosing a particular action. If you can subtly get your opponent to not throw rock, then you choose scissors (leads to either a tie or a win). Manipulation comes in many flavors. For instance, tell your opponent what you are going to throw and then actually do it. As they will likely not expect you to be that fearless and honest, the one thing that they probably won’t throw down is the action that beats yours. If you say, “rock," your opponent will likely throw rock or scissors, leading to your victory or tie. Another subtle manipulation technique derives from neurolinguistic programming. At the start of the game, remind someone about the rules. You might say, “Scissors beats paper, paper beats rock (show a sample of the rock with arm movement), and rock crushes scissors” (demonstrate how the rock crushes the scissors). In magic, this is called a “force.” Now expect them to throw down a rock. Obviously, you’ll answer with paper.
7. Remember that no one likes to be predictable. If someone has already thrown a double (typically because they won the first time with it), they are very unlikely to use it for a third time. If they used scissors twice, their next move will either be rock or paper. Paper is your best move to either win or tie. If they do two rocks, you follow with scissors. Two papers, you answer with rock.
8. Know the stats. Statistically, the expected average is 33.3 percent if everything is completely random. it turns out that the most common throw is rock (35 percent), scissors (35 percent), and then paper (29.6 percent). Not sure what to do next? Picking paper may give you a very slight advantage.
9. Be mindful. Observe your opponent’s hands before he throws. A tight hand, when raised often, ends in a rock. A loose hand becomes a paper and the first two fingers loose results in scissors. Closely observe your opponent as he or she plays RPS against others, do they tend to fall back on one particular throw? Is there a pattern? Do they telegraph their throw by moving their fingers early?

As a result of RPS contests, many complex algorithms have been developed with heuristically designed strategies, sub-strategies and meta-strategies based on past performances, frequency analysis, history matching, multi-history matching, and even random guessing.

Of course, if you were fortunate enough to have very keen observational skills and lightning-fast reflexes, you’d have an amazing advantage. When the robot hand from the University of Tokyo plays RPS, it uses a high-speed camera to recognize within one msec. which shape the human hand is making, and delivers the winning shape 100 percent of the time.

Source: Public Domain

What Does This All Mean in Terms of Real Life?

• In 2005, Takashi Hashiyama decided to auction off a collection of impressionist paintings worth tens of millions of dollars, including works by Cézanne, Picasso, and van Gogh. He contacted Christie's and Sotheby's auction houses. Hashiyama had the firms play RPS for who would get the auction rights. Christie's consulted the 11-year-old twin daughters of one of their directors, who suggested "scissors" because "Everybody expects you to choose rock." Sotheby's treated it as a random game of chance, had no particular strategy, and chose "paper." Christie's won and sold the $20 million collection, earning millions of dollars of commission.
• In 2006, Federal Judge Gregory Presnell from the Middle District of Florida ordered opposing sides in a lengthy court case to settle an issue using RPS.
• Warfare often involves RPS situations. For example cavalry over archers, archers over long spearman (pikemen), pikemen over cavalry. Many modern video games and card-based video games emulate this RPS cycle when choosing possible weapons or unit types. This phenomenon maintains gameplay and decreases the possibility of a significantly dominant strategy.
• In 2015, three officers were reprimanded when they allowed an underage drinker at a concert to try to avoid a ticket by winning at RPS.
• The RPS schema plays a role in bacterial ecology and evolutionary modeling. Intragenomic conflict arises when certain genes (called selfish elements) cause their own transmission to the detriment of the rest of the genome. Instead of the traditional Medelian frequencies in a general evolutionary model, we have RPS dynamics.
• There are many national and international RPS competitions with purses in the thousands of dollars.

Whether you compete for money, to get out of doing the dishes, or to avoid being the one to do push-ups, don’t rely on chance: Incorporate some of these psychological strategies.

Check out my book, Making Lemonade: 101 Recipes to Convert Negatives into Positives.

How many possible outcomes are there for the experiment choosing a rock or a paper or a pair of scissors at random Brainly?

How many possible outcomes are there for the experiment of choosing a color of the rainbow at random What is the sample space?

Is Rock

How are Rock