1. A committee of 5 people is selected at random from a group of 16 men and 12 w
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1. A committee of 5 people is selected at random from a group of 16 men and 12 women. Find the probability that the committee contains at least 2 women. (Set up, but do not evaluate.)
8. Four balls are selected at random without replacement from an urn containing four white balls and five blue balls. Find the probability of the given event.
Two or three of the balls are white.
2. According to a survey of 176 retailers, 55% of them use electronic tags as protection against shoplifting and employee theft. If one of these retailers is selected at random, what is the probability that he or she uses electronic tags as anti-theft devices? a. 0.54 b. 0.57 c.0.55 d. 0.56 3. What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 30 sec, the yellow signal for 5 sec, and the green signal for 40 sec? a. 0.30 b. 0.60 c. 0.50 d. 040 4. Given events A and B, if P(A) = .70, P(B) = .5, and P(A n B)=.28, then P(A | B) equals: a. 0.196 b. 0.560 c. 0.140 d. 0.400 5. John owns stock in 6 different companies. If the probability that at least one of the companies will go bankrupt is .18, then the probability that none of the companies will go bankrupt is: a. 0.18 b. 0.82 c. 0.88 d. 0.03 6. Two cards are drawn without replacement from a well-shuffled deck of 36 playing cards. What is the probability that the second card drawn is a spade given that the first card drawn was not a spade? What is the probability that the second card drawn is a spade given that the first card drawn was a spade? a. 1/12, 12/25 b. 5/6, 43/44 c. 5/11, 1/43 d. 9/35, 8/357. The James gang and Butch Cassidy's gang, each having 6 and 5 members, respectively, have gathered for the annual Bank Robbers Reunion. If the members are arranged at random for a photo, what is the probability that all the James gang will be on the left and the Cassidy gang on the right? (Set up, but do not evaluate.) a. 6!5!/11! b. 6!5!/ C(11,6) c. C(6,6) C(5,5)/ C(11,11) d. C(6,6) C(5,5)/11!
8. Four balls are selected at random without replacement from an urn containing four white balls and five blue balls. Find the probability of the given event.
Two or three of the balls are white.
a. 0 b. 1/18 c. 23/63 d. 40/63Explanation / Answer
q2)
given that 55% of 176 = 96.8 use tags
Therefore the probability = 96.8/176
= 12.1/ 22
=0.55
q3) 30/(30+40+5)
=30/75
=0.40
q4) P(A | B) =P(A n B)/P(B)
=0.28/0.50
=0.56
q5)the probability that none of the companies will go bankrupt is =1-(the probability that at least one of the companies will go bankrupt)
=1-0.18
=0.82
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