contestada

If the probability of one event occurring is .40 and the probability of a second event occurring is 0.60, then the probability that both events will occur must be 1.0 since that is the maximum value a probability can be. select one:
a. True
b. False

Respuesta :

Let [tex] P(A)=0.4 [/tex] and [tex] P(B)=0.6 [/tex]. The the probability both events occurring [tex] P(AB)=P(A)P(B|A)=P(B)P(A|B) [/tex].

This shows [tex] P(AB) \leq \min(P(A),P(B)) \\
P(AB) \leq \min(0.4,0.6)\\
P(AB) \leq 0.4 [/tex]

If A and B are independent

[tex] P(AB)=P(A)P(B)=0.4*0.6=0.24 [/tex]

Thus, the statement is (B) False.

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