Page 147 - Probability Demystified

136 CHAPTER 8 Other Probability Distributions

ANSWERS

1. a ¼ 5, b ¼ 7, n ¼ 5, x ¼ 2, n x ¼ 5 2 ¼ 3
2
7
The probability is 5 C C 3 ¼ 10 35 0:442
12 C 5 792
2. a ¼ 10, b ¼ 8, n ¼ 6, x ¼ 3, n x ¼ 3
C C 120 56
10 3 8 3
The probability is ¼ 0:362
18 C 6 18; 564
3. a ¼ 6, b ¼ 4, n ¼ 3, x ¼ 3, n x ¼ 3 3 ¼ 0
C C 0 20 1
3
6
4
The probability is ¼ ¼ 0:167
10 C 3 120
4. a ¼ 5, b ¼ 4, n ¼ 3, x ¼ 3, n x ¼ 3 3 ¼ 0
4
3
The probability is 5 C C 0 ¼ 10 1 0:119
9 C 3 84
5. a ¼ 3, b ¼ 3, n ¼ 2, x ¼ 2, n x ¼ 2 2 ¼ 0
C C 3 1
3 2 3 0
The probability is ¼ ¼ 0:2
6 C 2 15

The Geometric Distribution

Suppose you flip a coin several times. What is the probability that the first
head appears on the third toss? In order to answer this question and other
similar probability questions, the geometric distribution can be used. The
formula for the probability that the first success occurs on the nth trial is
n 1
ð1 pÞ p
where p is the probability of a success and n is the trial number of the first
success.

EXAMPLE: A coin is tossed. Find the probability that the first head occurs
on the third toss.

SOLUTION:
1
The outcome is TTH; hence, n ¼ 3 and p ¼ , so the probability of getting two
2
1
1
1
1
tails and then a head is ¼ .
2 2 2 8