1. Four balls are selected at random without replacement from an urn containing
ID: 3293309 • Letter: 1
Question
1.
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. 40/63
e. 83/126
f. 1
2. 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, 8/35
3.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!
Explanation / Answer
there are 9 balls in total , so 4 balls can be selected in 9C4 ways
2 white balls out of 4 white balls in can be selected in 4C2 ways and 3 balls can be selected in 4C3 ways
so the probability is
(4C2*5C2 + 4C3*5C1)/9C4 = (6*10+4*5 )/126 = 80/126 = 40/63, hence correct answer is d
=
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