Two events [math: P] and [math: Q] have probabilities given by Pr[math: (P)] [math: =0.53] = 0.53 and Pr[math: (Q)] [math: =0.19] = 0.19 .If the events [math: P] and [math: Q] are mutually exclusive, Pr[math: (P] U [math: Q)] is equal to:单项选择题
A
A. 0.62
B
B. 0.10
C
C. 0.34
D
D. 0.72

Question

Two events [math: P] and [math: Q] have probabilities given by Pr[math: (P)] [math: =0.53] = 0.53 and Pr[math: (Q)] [math: =0.19] = 0.19 .If the events [math: P] and [math: Q] are mutually exclusive, Pr[math: (P] U [math: Q)] is equal to:单项选择题

A

A. 0.62

B

B. 0.10

C

C. 0.34

D

D. 0.72

BlackTom AI · Accepted Answer

To approach this question, we first identify the given probabilities and the relationship between the events.
Option A: 0.62. This would imply a sum of 0.62 for P(P) and P(Q), which is not consistent with the provided individual probabilities: 0.53 for P and 0.19 for Q would sum to 0.72 if mutually exclusive. Therefore 0.62 is incorrect.
Option B: 0.10. This value is far smaller than either individual probability, and mutual exclusivity would not reduce the total probability below the highest single event nor produce such a small sum when adding the two probabilities. Hence this is not correct.
Option C: 0.34. This is close to the difference or a product-like figure, but for mutually exclusive events the probability of P or Q is the sum of their probabilities, not a product or adjusted value. Since P(P)=0.53 and P(Q)=0.19, their sum is 0.72, not 0.34, so this option fails.
Option D: 0.72. When two events are mutually exclusive, the probability of their union is P(P) + P(Q). Substituting the given values yields 0.53 + 0.19 = 0.72. This aligns with the fundamental rule for disjoint events, so this option is consistent with the information provided.
In summary, we evaluate each option against the basic probability rule for mutually exclusive events: P(P ∪ Q) = P(P) + P(Q). The only option that matches the computed sum is 0.72, while all other choices contradict either the additive rule or the given probabilities.

Two events [math: P] and [math: Q] have probabilities given by Pr[math: (P)] [math: =0.53] = 0.53 and Pr[math: (Q)] [math: =0.19] = 0.19 .If the events [math: P] and [math: Q] are mutually exclusive, Pr[math: (P] U [math: Q)] is equal to:单项选择题

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