MATH 1108 Homework
Han-Bom Moon
Homework 3 Solution
Section 8.1 and 8.2.
• Write your answer neatly.
• You may discuss with your classmates. But do not copy directly.
• You have to explain how you deduced your answer. Explain your notations, and
show computational steps.
1. A controversy arose in 1992 over the Teen Talk Barbie doll, each of which was
programmed with four sayings randomly picked from a set of 270 sayings. The
controversy was over the saying, “Math class is tough,” which some felt gave a
negative message toward girls doing well in math. We want to find the probability that a randomly chosen Barbie doll has the saying “Math class is tough.”
(a) What is the appropriate sample space in this probability computation? Count
the number of elements of the sample space.
The sample space is the set of all 4-selection of 270 sayings, without regarding the order. In other words, it is the combination of 270 sayings taken 4 at
a time.
(270)!
n(S) = 270 C4 =
= 216, 546, 345.
4!(270 − 4)!
(b) Find the probability.
M : event that the chosen Barbie doll has the saying “Math class is tough.”
To count n(M ), it is sufficient to count number of ways to choose 3 sayings
from 269, because the one “Math class is tough.” is already taken.
n(M ) = 269 C3 =
P (M ) =
269!
= 3, 208, 094.
3!(269 − 3)!
n(M )
3208094
=
≈ 0.0148.
n(S)
216546345
(c) In an interview with Science, a spokeswoman for Mattel, the makers of Barbie, said that “There’s a less than 1% chance you’re going to get a doll that
says math class is tough.” Is this figure correct? If not, give the correct figure.
The probability that a randomly selected Barbie doll has “Math class is tough”
is approximately 1.48% ,which is higher than 1%. So her analysis is incorrect.
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