P(B)= 9/20 P(A and B)= 9/100 P(A)=?

2 Answers
Apr 12, 2018

P(A)=1/5P(A)=15

Explanation:

Assuming events AA and BB are independent, we use

"P"(A nn B) = "P"(A) * "P"(B)P(AB)=P(A)P(B)

"         "9/100 = "P"(A) * 9/20         9100=P(A)920

20/9 * 9/100 = "P"(A)2099100=P(A)

"         "20/100="P"(A)         20100=P(A)

"             "1/5="P"(A)             15=P(A)

Apr 30, 2018

P(A) = 1/5P(A)=15

Explanation:

multiplication rule for probabilities:

P (A and B) = P(A) * P(B)P(AandB)=P(A)P(B)

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P (B) = 9/20P(B)=920

P (A and B) = 9/100P(AandB)=9100

P (A) = (P(A and B))/(P(B))P(A)=P(AandB)P(B)

(P(A and B))/(P(B)) = 9/100 div 9/20P(AandB)P(B)=9100÷920

= 9/100 * 20/9=9100209

= ((cancel9)1)/((cancel100)5) * ((cancel20)1)/((cancel9)1)

= (1 * 1)/(5 * 1)

= 1/5

hence, P(A) = 1/5.

this can be checked by applying the multiplication rule again:

P(A) * P(B) = 1/5 * 9/20 = (1 * 9)/(5 * 20) = 9/100

P (A and B) = 9/100