Question

the numbers 1, 2, 3, 4, and 5 are written on slips of paper, and 2 slips are drawn at random one at a time without replacement. (a) find the probability that the first number is 4, given that the sum is 9. (b) find the probability that the first number is 2, given that the sum is 6. (a) the probability that the first number is 4, given that the sum is 9 is (simplify your answer.)

Explanation:

Step1: List pairs with given sums

For sum = 9, pairs are (4, 5) and (5, 4). For sum = 6, pairs are (2, 4) and (4, 2).

Step2: Calculate conditional probabilities

For part (a), there are 2 pairs with sum 9, and 1 pair has 4 as first - number. Probability = $\frac{1}{2}$.
For part (b), there are 2 pairs with sum 6, and 1 pair has 2 as first - number. Probability = $\frac{1}{2}$.

Answer:

(a) $\frac{1}{2}$
(b) $\frac{1}{2}$