Question

numbers are chosen at random.
a. find the probability of selecting an odd number.
b. find the probability of selecting a prime number.
c. find the probability of selecting a number that is prime and odd.
d. find the probability of selecting a number that is not odd or prime.

1. the venn diagram shows information about if students like cricket and rugby. students are selected at random.

a) find the probability that the student selected like cricket and rugby.
b) find the probability that the student selected doesn’t like either sport.

Explanation:

Problem 1 (Assuming the set of numbers is not provided, but we can solve Problem 2 first as the Venn diagram data is given)

Problem 2:

First, we need to find the total number of students. The numbers in the Venn diagram are: only Cricket = 15, both Cricket and Rugby = 35, only Rugby = 27, and neither = 12.

Total number of students, \( n(\xi) = 15 + 35 + 27 + 12 = 89 \)

Part a)

We need to find the probability that a student likes both cricket and rugby. The number of students who like both is 35.

Step 1: Identify favorable and total outcomes

Favorable outcomes (like both) = 35, Total outcomes = 89

Step 2: Calculate probability

Probability \( P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{35}{89} \)

Step 1: Identify favorable and total outcomes

Favorable outcomes (don't like either) = 12, Total outcomes = 89

Step 2: Calculate probability

Probability \( P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} = \frac{12}{89} \)

Answer:

\(\frac{35}{89}\)

Part b)

We need to find the probability that a student doesn't like either sport. The number of students who don't like either is 12.