Question

Find the conditional probability of the indicated event when two fair dice (one red and one green) are rolled. The red one is 1 , given that the sum is 5 . 5. [-/1 Points] WANEFMAC7 8.5.023. event. he gets all the red ones, given that she gets the fluorescent pink one.

Answer 1

The conditional probability that the red die shows a 1, given that the sum of two dice is 5, is 0.25 or 1/4.

Step-by-step explanation:

We are asked to find the conditional probability that the red die shows a 1, given that the sum of two dice is 5. Let's denote the event 'the red die is 1' as R1 and the event 'the sum is 5' as S5. The probability of R1 given S5 can be represented as P(R1|S5).

To calculate P(R1|S5), we should first consider all the possible ways to get a sum of 5 when rolling two dice: (1,4), (2,3), (3,2), (4,1). Note that these pairs are ordered pairs where the first number corresponds to the red die and the second to the green die. Among these, only one outcome has the red die showing a 1, which is (1,4).

The conditional probability is therefore the count of favorable outcomes for R1 within the S5 events divided by the total number of S5 events. So we get:

P(R1|S5) = Number of favorable outcomes for R1 in S5 / Total number of outcomes in S5

P(R1|S5) = 1/4

Thus, the conditional probability is 1 out of 4, or 0.25.