MHB What value of p makes A and B mutually exclusive events?

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To determine the value of p that makes events A and B mutually exclusive, it is established that P(A & B) must equal 0. Given P(A) = 0.4 and P(A or B) = 0.8, the formula P(A or B) = P(A) + P(B) - P(A & B) simplifies to P(A or B) = P(A) + P(B) when A and B are mutually exclusive. Substituting the known values leads to the equation 0.8 = 0.4 + p. Solving this gives p = 0.4, indicating that for A and B to be mutually exclusive, the value of p must be 0.4. This conclusion clarifies the conditions for mutual exclusivity in probability.
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Here's another probability question that's confusing me, any help would be appreciated!

Let A and B be two events with P(A) = 0.4, P(B) = p, and P(A or B) = 0.8. For what value of p will A and B be mutually exclusive? (Round to four decimal places as appropriate.)
 
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das said:
Here's another probability question that's confusing me, any help would be appreciated!

Let A and B be two events with P(A) = 0.4, P(B) = p, and P(A or B) = 0.8. For what value of p will A and B be mutually exclusive? (Round to four decimal places as appropriate.)

Two events A and B are mutually exclusive if P (A & B)=0. In general is P(A or B) = P(A) + P(B) - P(A & B), so that...

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That was the formula I wanted, thanks!
 
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