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. Find the given probabilities.
(a) The sum of the numbers is 8.
(b) The sum of the number is 6 or less.
(c) The first number is 2 or the sum is 5.

Answer 1

Answer:

(a) P(sum is 8) = 1/20

(b) P(sum is 6 or less) = 3/10

(c) P(first number is 2 or the sum is 5) = 3/10

Step-by-step explanation:

(a)

The probability (P) of having 8 as the sum of the numbers is;

P(3 and 5) = 1/5 × 1/4 = 1/20

(b) Probability that the sum of the numbers is 6 or less.

P(sum is 6) = P(2 and 4) or P(1 and 5) = 1/20 + 1/20 = 1/10

P(sum is less than 6) = P(1 and 4) or P(1 and 3) or P(1 and 2) or P(2 and 3) = 1/20 × 4 = 1/5

P(sum is 6 or less) = 1/10 + 1/5 = 3/10

(c) The first number is 2 or the sum is 5

P(first number is 2) = 1 - P(first number is 1) - P(first number is 3) - P(first number is 4) - P(first number is 5) = 1 - 4(1/5) = 1/5

P(sum is 5) = P(1 and 4) or P(2 and 3) = 1/20 + 1/20 = 1/10

P(first number is 2 or sum is 5) = 1/5 + 1/10 = 3/10