Answer
a. In each of the four tosses there are two possible results:
Either a head (H) or a tail (T ) is obtained. Thus, by the
multiplication rule, the number of outcomes is
2·2·2·2 = 24 = 16.
b. There are six outcomes with two heads:
HHTT, HTHT, HTTH, THHT, THTH, TTHH.
Thus the probability of obtaining exactly two heads is
6/16 = 3/8.
c. There are four outcomes with one head:
HTTT, THTT, TTHT, TTTH.
Thus the probability of obtaining exactly two heads is
4/16 = 1/4.
Work Step by Step
a. In each of the four tosses there are two possible results:
Either a head (H) or a tail (T ) is obtained. Thus, by the
multiplication rule, the number of outcomes is
2·2·2·2 = 24 = 16.
b. There are six outcomes with two heads:
HHTT, HTHT, HTTH, THHT, THTH, TTHH.
Thus the probability of obtaining exactly two heads is
6/16 = 3/8.
c. There are four outcomes with one head:
HTTT, THTT, TTHT, TTTH.
Thus the probability of obtaining exactly two heads is
4/16 = 1/4.