U and V are mutually exclusive events.P(U) = 0.28P(V) = 0.33Part (a)P(U AND V) = Part (b)P(U | V) = Part (c)P(U OR V) =
Question
U and V are mutually exclusive events.
- P(U) = 0.28
- P(V) = 0.33
Part (a)
- P(U AND V) =
Part (b)
- P(U | V) =
Part (c)
- P(U OR V) =
Solution
Part (a) Since U and V are mutually exclusive events, they cannot occur at the same time. Therefore, the probability of both U and V occurring, denoted as P(U AND V), is 0.
Part (b) The conditional probability of U given V, denoted as P(U | V), is the probability of event U occurring given that event V has already occurred. However, since U and V are mutually exclusive, if V has occurred, U cannot occur. Therefore, P(U | V) is also 0.
Part (c) The probability of U or V occurring, denoted as P(U OR V), is the sum of the probabilities of U and V. This is because U and V are mutually exclusive, so there's no overlap to subtract out. Therefore, P(U OR V) = P(U) + P(V) = 0.28 + 0.33 = 0.61.
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