Page 129 - Probability Demystified

118 CHAPTER 7 The Binomial Distribution

EXAMPLE: A coin is tossed 3 times. Find the probability of getting two
heads and a tail in any given order.

SOLUTION:

Since the coin is tossed 3 times, n ¼ 3. The probability of getting a head (suc-
1
1
1
1
cess) is ,so p ¼ and the probability of getting a tail (failure) is 1 ¼ ;
2 2 2 2
x ¼ 2 since the problem asks for 2 heads. (n x) ¼ 3 2 ¼ 1.
Hence,
1
2
1 1
Pð2 headsÞ¼ C 2 2
3
2

1 1
¼ 3
4 2
3
¼
8
Notice that there were 3 C 2 or 3 ways to get two heads and a tail. The
answer 3 is also the same as the answer obtained using classical probability
8
that was shown in the first example in this chapter.
EXAMPLE: A die is rolled 3 times; find the probability of getting exactly
one five.

SOLUTION:
1
Since we are rolling a die 3 times, n ¼ 3. The probability of getting a 5 is .
6
5
1
The probability of not getting a 5 is 1 or . Since a success is getting
6 6
one five, x ¼ 1 and n x ¼ 3 1 ¼ 2.
Hence,
2
1
1 5
Pðone 5Þ¼ C
1
3
6 6
1 25
¼ 3
6 36
25
¼ or 0:3472
72
About 35% of the time, exactly one 5 will occur.