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vovikov84 [41]
1 year ago
14

If p(a | b) = 0.4, p(b) = 0.8, and p(a) = 0.5, are the events a and b independent?

Mathematics
1 answer:
pashok25 [27]1 year ago
7 0

The events A and B are not independent.

Given that,

                  P(A|B) = 0.4

                  P(A) = 0.5

                  P(B) = 0.8

Two events A and B are said to be independent, if P(A∩B) = P(A) P(B)

We have, P(A|B) = P(A∩B)/P(B)

Therefore, P(A∩B) = P(A|B) P(B) = 0.4 x 0.8 = 0.32

Now P(A) P(B) = 0.5 x 0.8 = 0.4

So P(A∩B) ≠ P(A)P(B)

Therefore, the events A and B are not independent.

Learn more about independent events at brainly.com/question/22881926

#SPJ4

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   The probability of getting into getting into graduated school if you receive a strong recommendation is  P(G |S) = 0.80

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      Generally  the probability that you will get into a graduate program is mathematically represented as

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Generally  given that you did receive an offer to attend a graduate program, what is the probability that you received a strong recommendation is mathematically represented as

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         P(M| G') =  \frac{ 0.2 *  (1- 0.6)}{ (1 - 0.69)}

         P(M|G') =  0.26

 

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