Answer:
because is the probability is 0.17 and 0.34 is fair
You can use the multiplication rule of probability.
The probability of event B happening if event A has already happened is 0.5
[tex]P( A \: \rm and \: B) = P(A)P(B|A) = P(B)P(A|B)[/tex]
Since we've to find the probability of B given that A has already happened, we need [tex]P(B|A)[/tex]
Since the probability of both event A and event B happening simultaneously is 0.17, thus:
[tex]P(A \: \rm and \: B) = 0.17\\
[/tex]
Since the probability of only event A happening is 0.34, thus:
[tex]P(A) = 0.34[/tex]
Thus, from the multiplication rule, we have:
[tex]P(A \: \rm and \: B) = P(A)P(B|A)\\
0.17 = 0.34 \times P(B|A)\\\\
\dfrac{0.17}{0.34} = P(B|A)\\\\
P(B|A) = \dfrac{1}{2} = 0.5[/tex]
Thus, we have the probability of event B happening when A has already happened as 0.5
Learn more about multiplication rule of probability here:
https://brainly.com/question/14450597
