Answer:
0.875 is the required probability.
Step-by-step explanation:
We are given the following in the question:
Probability Billy would pass atleast one test = 0.9
[tex]P(A\cup B) = 0.9[/tex]
Probability Billy would pass both test = 0.7
[tex]P(A\cap B) = 0.7[/tex]
The two test are equally difficult.
[tex]P(A) = P(B)[/tex]
For independent events we can write that
[tex]P(A\cup B) = P(A) + P(B) -P(A\cap B)\\0.9 = 2P(A) - 0.7\\2P(A) = 1.6\\P(A) = P(B)=0.8[/tex]
We have to find the conditional probability that Billy passing test 2 given the event that he passes test 1.
[tex]P(B|A) = \dfrac{P(B\cap A)}{P(A)} = \dfrac{0.7}{0.8} = 0.875[/tex]
0.875 is the conditional probability of Billy passing test 2 given the event that he passes test 1
