Answer :
Answer:
When Mary raises the probability that she has a better hand is 0.273
Step-by-step explanation:
In the poker game it is given that the probability that Mary has a better hand than John is 0.04.
Let the event that Mary has a better hand than John be A.
Let the event that that Mary raises the stakes be B.
It is also given that if Mary has a better hand than John then she would raise with a probability of 0.9
Therefore p(B | A) = 0.9
If Mary has a poorer hand she will raise with a probability of 0.1
Therefore p(B | A') = 0.1
Given that Mary raises the probability that she has a better hand is given by
p(A | B)
[tex]= \frac{p(A\cap B)}{p(B)}[/tex] = [tex]\frac{p(A)p(B | A)}{p(A)p(B | A) + p(A')p(B | A')} = \frac{(0.04 \times 0.9) }{(0.04 \times 0.9) + (0.96 \times 0.1)} = \frac{36}{36 + 96} = \frac{36}{132} = \frac{3}{11}[/tex]
= 0.273
So when Mary raises the probability that she has a better hand is 0.273