1. If, for example, two coins are tossed together, then the chance for each falling with
heads up is 1/2. Likewise, the chance for tails is ½, therefore, the chance that both will be
heads is____ __
. The chance for the first coin to fall heads and the second coin tails is
, but one head and one tail can be obtained in another way: The first coin
could be tails and the second heads. Therefore, the total probability of obtaining a head on
one coin and a tail on the other is _______
. The chance for both coins to fall tails up is the
same as for both to be heads, that is, _______
. To summarize, two coins tossed together
many times are expected to fall heads, heads about _______
of the time; heads, tails (and
vice versa) about _______
of the time; and tails, tails about _______
of the time. Stated
as a ratio instead of as fractions, the expected result is _______
2. Write in the letters (H and T) to represent the coins in the "Combinations" column, and
calculate the probability for each class resulting when four coins are tossed.
Each Class Occuring
3. Assuming that the probability that a boy will be born is 1/2 and that the chance for a girl is
also 1/2, answer the following questions,
a. If four babies are born in a given hospital on the'same day, what is the probability that all
four will be boys?
b. What is the probability that three will be boys and one a girl?
c. What is the probability that two will be boys and two girls?
d. What combination of boys and girls among the four babies is most likely to occur?
e. What is the probability that if a fifth child is born it will be a boy? A girl?.
Expectations for various combinations in groups of given size («) can be obtained
mathematically. Mendel and others recognized that combinations can be calculated by
expanding the binomial (a + b)
, in which n is the size of the group, a is the probability
of the first event, b is the probability of the alternative event, and a + b = 1. In the
example involving babies, a — probability of girls = 1/2 and b = probability of boys =
1/2. Now, if you wish to consider the case in which four babies are born in the hospital
in 1 day, expand (a + b)
b + 6a