Question

1. Let the sample space represent all the values from 1 to 10. Let A = {1, 2, 8} and B = {2, 7}. What is the P(A ∩ B)?

Answer 1

A
`\cap` B denotes to all common elements in both A and B

• Sample space=S={1,2,3,4,5,6,7,8,9,10}

So

• A={1,2,8}
• B={2,7}

2 is common

Hence

A $\cap$ B={2}

Answer 2

P(A ∩ B) = 1/10

Explanation:

Given:

• Sample space (S) = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
• A = {1, 2, 8}
• B = {2, 7}

We can represent this information in a Venn diagram (see attachment 1).

As there are 10 equally likely outcomes (which must add up to 1), the probability of each outcome is 1/10.

Therefore, we can redraw the Venn diagram with the probabilities instead of the values (see attachment 2).

P(A ∩ B) means the probability of events A and B happening together, so it is the section of the diagram where events A and B overlap.

Therefore, P(A ∩ B) = 1/10