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.

(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