Suppose that P(A|B)=0.2, P(A|B')=0.3, and P(B)=0.7. What is the P(A)? Round your answer to two decimal places (e.g. 98.76).

Question

asked Sep 11, 2021 115k views

1 Answer

Johan De Klerk · Answer 1 · 2021-09-15T01:29:44+0000

Answer:
P(A) = 0.23

Explanation:

Given :

P(A/B) = 0.2

P(A/B^(1))=0.3

P(B)= 0.7

P(A) = ?

From rules of probability :

P(A) = P(AnB) + P(A n B^(1)) ........................... equation *

P(A n B) can be written as
P(A/B) x
P(B)

Also ,
P(A/B^(1)) can be written as
x
P(B^(1))

substituting into equation * , we have

P(A) = P(A/B)
P(B) + P(A/B^(1))P(B^(1))

since P(B) = 0.7, then
P(B^(1)) = 1 - P(B) = 0.3

so , substituting each values , we have

P(A) = (0.2)(0.7) + (0.3)(0.3)

P(A) = 0.14 + 0.09

P(A) = 0.23