0824/0924 Second Quiz and Answers
Ten points for each problem.
1a.) A family plans on having 4 children. List the 16 elements of the sample space.
1b.) What is the probability there will be three boys and one girl?
1c.) If the family has at least 1 girl, what is the probability it has exactly 3 girls?
a.) the usual array of the 16 possibilities methodically listed
b.) 4/16, obtained by counting up the four ways they can have 3 boys and a girl
c.) 4/15, since the BBBB possibility is ruled out leaving 15 possibilities of which 4
have exactly 3 girls
2a.) Two dice are rolled. List the 36 elements of the sample space.
2b.) What is the probability the sum of the dice is 2, 3, or 4? What is the probability
the sum is 12? What is the probability the sum is one of the remaining numbers: 5, 6,
7, 8, 9, 10, or 11?
2c.) If the sum is 2, 3, or 4, you win $10; if the sum is 5 through 11, you win $30; and
if the sum is 12, you lose $300. What are your expected winnings per play?
a.) the usual 36 possibilities
b.) P(2,3, or 4) = 6/36 since 2, 3, or 4 can occur in any one of 6 ways; P(12) = 1/36;
P(5,6,7,8,9,10, or 11)=1 - (6/36+1/36) = 29/36 or by counting all the 29 ways
6,7,8,9,10, or 11 can come up
c.) plug into formula for expected value: $10*(6/36) + $30*(29/36) - $300*(1/36) =
$17.50
3a.) A roulette wheel has 18 red, 18 black, and 2 green sectors. What is the
probability of landing on red 6 times in a row?
3b.) What is the probability of not landing on green in 6 spins of the roulette wheel?
3c.) What is the probability of landing on green at least once in 6 spins?
a.) (18/38)6 , which =.011 or 1.1%
b.) (36/38)6 , which = .723 or 72.3%
c.) 1 - (36/38)6, which = .277 or 27.7%, since b.) and c.) ask about complementary
events.
4a.) Three hunters independently shoot at a target. The first hits 60% of the time,
the second 75%, and the third 90%. What is the probability they all hit it?
4b.) What is the probability they all miss it?
4c.) What is the probability at least one hits it?
a.) (.60)(.75)(.90) = .405 or 40.5%
b.) (.4)(.25)(.10) = .01 or 1%
c.) 1-.01 = .99 or 99%, since b.) and c.) ask about complementary events.
5a.) What is the probability that the sum of two dice is 11?
