The governors of three states appoint a crime commission that includes 12 Florid
ID: 3307349 • Letter: T
Question
The governors of three states appoint a crime commission that includes 12 Floridians (8 of whom are women), 9 residents of Alabama (6 of whom are women), and 10 Georgians (7 of whom are women).
a.) If the chairperson is randomly selected, find the probability of getting a woman.
b.) If the chairperson is randomly selected, find the probability of getting a man or a Floridian.
c.) If two different members are randomly selected for a special project, find the probability that they are both women. Assume that a woman was selected for the first draw.
d.) At each meeting, one of the members is randomly chosen to be secretary. Find the probability that the first two secretaries are both men. (Note: The same man could be chosen both times.)
Explanation / Answer
Total people in crime commission is computed as: = 12 + 9 + 10 = 31
a) Probability of getting a woman as a chairperson is computed as:
= Number of women in the crime commission / Total people in the crime commission
= (8 + 6 + 7 ) / 31
= 0.6774
Therefore 0.6774 is the required probability here.
b) Number of man = 31 - 21 = 10. Number of floridan who are not man = 8 . Therefore number of people who are either man or floridans is computedas = 10 + 8 = 18
Therefore the required probability here is computed as:
= 18/31
= 0.5806
Therefore 0.5806 is the required probability here.
c) Given that a woman was selected for the first draw, we are left with 20 women and 10 men now. Probability that both now selected would be women is computed as:
= number of women left / Total number of people left
= 20 / 30
= 0.6667
Therefore 0.6667 is the required probability here.
d) Probability that the first two secretaries are both men is computed as:
= Probability of selecting a man * Probability of selecting a man
= (10/31)*(10/31)
= 0.1041
Therefore 0.1041 is the required probability here.
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