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 4 or less. c. the first number is 2 or the sum is 5. a. the probability that the sum of the numbers is 8 is (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total number of outcomes

The number of ways to draw 2 - slips out of 5 without replacement is given by the permutation formula $P(n,r)=\frac{n!}{(n - r)!}$, where $n = 5$ and $r=2$. So, $P(5,2)=\frac{5!}{(5 - 2)!}=\frac{5!}{3!}=5\times4 = 20$ outcomes.

Step2: Find pairs with sum 8

The pairs of numbers that sum to 8 are $(3,5)$ and $(5,3)$. So there are 2 favorable outcomes.

Step3: Calculate probability

The probability $P$ is the number of favorable outcomes divided by the total number of outcomes. So $P=\frac{2}{20}=\frac{1}{10}$.

Answer:

$\frac{1}{10}$