Probability 01.14.08

Probability Workshop 1

Question 1 A rack contains 15 dresses. Five of the dresses are blue, six are green, and four are yellow. If selling each of the dresses is equally likely, what is the probability that if six dresses are sold, exactly two will be green? 2

A rack contains 15 dresses. Five of the dresses are blue, six are green, and four are yellow. If selling each of the dresses is equally likely, what is the probability that if six dresses are sold, exactly two will be green? choose 4 from the choose 2 green dresses that are not green P(2G) = 6C2 9C4 choosing 6 dresses 15C6 from the rack = 15 126 5 005 = 1 890 5 005 = 0.377 or 37.8 % 3

Question 2 A couple intends to have 4 children. Assume that having a boy or a girl are equally likely events. Find the probability that the couple has atleast 2 girls. 4

A couple intends to have 4 children. Assume that having a boy or a girl are equally likely events. Find the probability that the couple has atleast 2 girls. Choose atleast 2 girls, it could be 2 girls and 2 boys or 3 girls and 1 boy, or 4 girls then add them. P (2G) = 4C2 + 4C3 + 4C4 4 (2C1) Choose the gender then multiply it 4 times because there are four children. = 11 16 5

Question 3 In a car lot, 25% of the inventory are SUV's, and 75% are passenger cars. 80% of SUV's, and 65% of the passenger cars, have air conditioning. What is the probability that a chosen vehicle will be an SUV given the vehicle has air conditioning? 6

In a car lot, 25% of the inventory are SUV's, and 75% are passenger cars. 80% of SUV's, and 65% of the passenger cars, have air conditioning. What is the probability that a chosen vehicle will be an SUV given the vehicle has air conditioning? P(SA) = (.25) (.80) = .2 S SUV P(PA) = (.75) (.35) = .4875 P Passenger Car P (SA) A with AC P(S|A) = N no AC A .80 P(SA) + P(PA) .2 S = N .20 .25 (.2) + (.4875) A .65 = .281 P .75 N .35 7

Afternoon Class continuation of the Probability Workshop 8

Question 4 A box of eight razor blades contains two defective blades. If two blades are drawn at random, with the first not replaced, what is the probability that exactly one of the two blades will be defective? 9

Solution: A box of eight razor blades contains two defective blades. If two blades are drawn at random, with the first not replaced, what is the probability that exactly one of the two blades will be defective? 2 6 = 12 N = Not Defective ND = 7 56 8 D = Defective 2 6 5 12 N DN = 7 = 56 7 8 N 12 12 = 56 + 56 2 6 D 7 8 24 N6 = 56 7 D 2 3 = 1 D 8 7 7 10

Question 5 If a biased coin is tossed 6 times, what is the probability of obtaining exactly 2 heads if the probability of getting heads on any one is 2/5? 11

Solution: If a biased coin is tossed 6 times, what is the probability of obtaining exactly 2 heads if the probability of getting heads on any one is 2/5? ( )( ) ( )( )( )( ) H = Heads 3 3 3 3 2 2 HHTTTT T = Tails 5 5 5 5 5 5 6! 2 4 ( )( ) 3 2 5 5 2!4! 4 tails number of different 2 heads ways that you can get 2 heads and 4 tails 12

Probability 01.14.08

by misz.shaneeey on Jan 15, 2008

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