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We have given the table of number of male and female contestants who did and did not win prize
The probability that a randomly selected contestant won prize given that contestant was female is
P(contestant won prize / Contestant was female)
Here we will use conditional probability formula
P(A/B) =
Let Event A = selected contestant won prize and
event B = selected contestant is famale
Then numerator entity will
P(A and B) = P(Contestant won prize and Contestant is female)
= Number of female contestant who won prize / Total number of contestant
= 3 /(4+9+3+10)
= 3 / 26
P(A and B) = 0.1153
P(B) = P(contestant is female )
= Number of female contestant / Total number of contestants
= (3+10) / 26
P(B) = 0.5
Now P(A / B) =
= 0.1153 / 0.5
P(A / B) = 0.2306
The probability that randomly selected contestant won prize given that contestant is female is 0.2306
Converting probability into percentage 23.06%
The percentage that randomly selected contestant won prize given that contestant is female is 23%
Using conditional probability, it is found that there is a 0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.
Conditional Probability
In which
- P(B|A) is the probability of event B happening, given that A happened.
is the probability of both A and B happening.
- P(A) is the probability of A happening.
In this problem:
- Event A: Person has the flu.
- Event B: Person got the flu shot.
The percentages associated with getting the flu are:
- 20% of 30%(got the shot).
- 65% of 70%(did not get the shot).
Hence:
The probability of both having the flu and getting the shot is:
Hence, the conditional probability is:
0.1165 = 11.65% probability that a person with the flu is a person who received a flu shot.
To learn more about conditional probability, you can take a look at brainly.com/question/14398287