SOLUTION: There are 20 people in a room, 15 men and 5 women. Ten of the men are 30 years of age or older and the other five are under 30. Four of the women are under 30 and one is over 30.

Question 470512: There are 20 people in a room, 15 men and 5 women. Ten of the men are 30 years of age or older and the other five are under 30. Four of the women are under 30 and one is over 30.

If I pick a person at random what is the probability of picking a man? A woman?

If I pick a person at random what is the probability the person will be male or over 30?

If I pick a person at random what is the probability the person will be female or under 30?

If I pick two people at random what is the probability of picking a man on the first pick and a woman on the second without replacement? What would the probability be with replacement?

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
If I pick a person at random what is the probability of picking a man? 15/20 = 3/4. A woman? 5/20 = 1/4.
If I pick a person at random what is the probability the person will be male or over 30? P(male U over 30) = P(male) + P(over 30) - P(male AND over 30) = 3/4 + 11/20 - 10/20 = 4/5.
If I pick a person at random what is the probability the person will be female or under 30? P(female U under 30) = P(female) + P(under 30) - P(female AND under 30) = 1/4 + 9/20 - 4/20 = 1/2.
If I pick two people at random what is the probability of picking a man on the first pick and a woman on the second without replacement? (15/20)*(5/19) = 15/76
What would the probability be with replacement? (15/20)*(5/20) = 3/16.

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