Question #335891

Suppose A and B are mutually exclusive events defined on the same sample space such that 𝑃(𝐴)=0.37 and 𝑃(𝐵)=𝑐.

Question 11

What is the maximum value of 𝑐?

Question 12

What is 𝑃(𝐴|𝐵)?


1
Expert's answer
2022-05-03T14:55:08-0400

Events A and B are mutually exclusive events,

P(A)+P(B)1,0.37+c1,c10.37,c0.63.P(A) +P(B) \le1, \\ 0.37+c\le1,\\ c\le1-0.37,\\ c\le0.63.

The maximum value of c is 0.63.


P(AB)=P(AB)P(B)=0P(B)=0.P(A|B) =\cfrac{P(A\cap B) } {P(B) } =\cfrac{0 } {P(B) }=0.

Mutually exclusive events can't happen simultaneously, so the probability of (A and B) is equal to zero.





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