MATH 111: HW 8 SOLUTIONS AND COMMENTS
7.1, #3. Since 53 out of 100 tosses came up heads, 100 −53 = 47 of them came up tails.
So, 47 out of 100, or 47%, of the tosses were tails.
7.1, #7. In case you’re curious, 1572 of the class’ 3100 spins came up heads, or approxi-
mately 50.7%.
7.1, #9. The king was found in 491 of the class’ 1250 trials, which is approximately 39%
of the trials.
7.2, #1. The probability that he wears the black shoes is 1 −3
5=2
5.
7.2, #2. There are four equally likely possible outcomes:
Dime Penny
H H
H T
T H
T T
Of these outcomes, the first three (HH, HT, TH) comprise the event that at least one head
is flipped. Therefore, the probability of this event is 3/4.
7.2, #3. There are a total of 14 chocoloates, each of which was equally likely to have
been picked. Therefore, the probability of picking a green chocolate was 2/14 = 1/7. The
probability of picking a blue chocolate was 5/14.
I like chocolate, so the probability that I would eat the chocolate is 1. This probability may
or may not be different for you!
7.2, #13. There are 6 equally likely outcomes of the die roll, and 2 equally likely outcomes
of the coin flip, so there are 6×2 = 12 equally likely outcomes for this experiment (in which a
die is rolled and independently a coin is flipped). The event that Roosevelt can be seen (i.e.,
the coin lands heads) and 4 is rolled is one of these 12 outcomes; therefore, the probability
of this event is 1/12.
If we’re told that the die roll was 2, then there are only two remaining possible equally likely
outcomes: 2 with heads; and 2 with tails. The dime lands tails in one of these two outcomes,
so the probability that the dime lands tails under these circumstances is 1/2.
7.2, #18. There are 38 equally likely outcomes (0, 00, and 1 through 36). The probability
of the single outcome 13 is therefore 1/38.
