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)?
2 answers:
A 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:
P(A ∩ B) = 1/10
Step-by-step 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
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