While playing Yahtzee, Amanda rolls five dice and gets 1, 2, 4, 5, 6. She decides to keep the 1, 2, and 4, and reroll the 5 and 6.
After rerolling the 5 and 6, what is the probability for a large straight (1-2-3-4-5) or three 4's?
Also, what is the probability for a small straight (1-2-3-4 plus anything else)or a pair of three's?
You asked this question earlier. It has already been answered
What you are being asked is what is the probability of getting 3 and 5 or two 4s on the next roll.
On the second problem, the probability of getting a 3 is 1/6 and "anything else" is 1. With the information below, you should be able to calculate the probability of a pair of 3s.
The probability of getting any particular number on a die is 1/6. The probability of getting both numbers is obtained by multiplying the individual probabilities. The probability of getting "either-or" is obtained by adding the probabilities.
I hope this helps. Thanks for asking.
From what drwls has said, I want to ask you to please only post your questions once. Repeating posts will not get a quicker response. In addition, it wastes our time looking over reposts that have already been answered in a previous post. Thank you.
To calculate the probability of getting a certain outcome in Yahtzee, we need to determine the number of favorable outcomes (the desired outcomes) and divide it by the total number of possible outcomes.
1. Probability of a large straight or three 4's:
A large straight consists of the numbers 1, 2, 3, 4, and 5 appearing in sequence. Three 4's would require at least three dice showing 4.
First, let's count the number of favorable outcomes for a large straight. Since Amanda is rerolling the 5 and 6, she needs either of them to be a 3 and replace the missing number. There are two ways this can happen: 5 becomes 3 (with the dice showing 1, 2, 3, 4, 3) or 6 becomes 3 (with the dice showing 1, 2, 3, 4, 3). So, there are two favorable outcomes for a large straight.
Next, let's count the number of favorable outcomes for three 4's. Amanda has already rolled 1, 2, 4, so she needs the two remaining dice to show 4. Since there are only two dice, there's only one way this can happen: the remaining two dice show 4. Therefore, there is one favorable outcome for three 4's.
Now, let's determine the total number of possible outcomes. Since Amanda is keeping the 1, 2, and 4, she is only rerolling the 5 and 6, which means there are 2^2 = 4 possible outcomes for those two dice.
Therefore, the total number of possible outcomes is 4.
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability for large straight or three 4's = (2 favorable outcomes) / (4 possible outcomes) = 2/4 = 1/2 = 0.5
2. Probability of a small straight or a pair of three's:
A small straight consists of the numbers 1, 2, 3, and 4 appearing in sequence, plus any other number on the fifth dice. A pair of threes requires at least two dice showing 3.
First, let's count the number of favorable outcomes for a small straight. Amanda has already rolled 1, 2, 4, so she needs the remaining dice (the rerolled 5 and 6) to show 3 and any other number. Since there are two dice, there are two ways this can happen: (3, X) or (X, 3), where X represents any number other than 3. Therefore, there are two favorable outcomes for a small straight.
Next, let's count the number of favorable outcomes for a pair of threes. Amanda has already rolled 1, 2, 4, and rerolled the 5 and 6, so she needs at least two dice showing 3. There are two ways this can happen: (3, 3) or (3, X), where X represents any number other than 3. Therefore, there are two favorable outcomes for a pair of threes.
The total number of possible outcomes for the dice remaining (5 and 6) is 4, as mentioned earlier.
Therefore, the total number of possible outcomes is 4.
To calculate the probability, we divide the number of favorable outcomes by the total number of possible outcomes:
Probability for small straight or pair of threes = (2 favorable outcomes) / (4 possible outcomes) = 2/4 = 1/2 = 0.5
So, the probability for both scenarios, large straight or three 4's, and small straight or pair of threes, is the same: 0.5 or 50%.