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Suppose we have a sample space S={a;b; c; d;e; f; g; h; i; j } and we have events:
A= {a;b; i; d;e} ; B= {c;a;g;e;d} and C ={c;h; i; e;f}
1 Calculate the probability A ∩ C.
2 Are the events B and C mutually exclusive? Explain.
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Suppose we have a sample space S={a;b; c; d;e; f; g; h; i; j } and we have events:
A= {a;b; i; d;e} ; B= {c;a;g;e;d} and C ={c;h; i; e;f}
1.    Calculate the probability A ∩ C.

A ∩ C = {i; e}

P(A ∩ C) = 2/10 = 1/5

2.    B ∩ C = {a; d; e}. Since B ∩ C is non-empty and has three elements, this means that events B and C are not mutually exclusive.

OR

P(B ∩ C) = 3/10 ≠ 0. Therefore B and C are not mutually exclusive events.
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