Sec. 4.3 The Geometric Distribution
A _______________ ______________ is a discrete probability distribution of a
random variable 𝑥 that satisfies the following conditions.
1. A trial is repeated until a success occurs.
2. The repeated trials are independent of each other.
3. The probability of success 𝑝 is constant for each trial.
The probability that the first success will occur on trial number 𝑥 is
𝑃(𝑥) = 𝑝(𝑞)𝑥−1 , where 𝑞 = 1 − 𝑝
Solve the following problems involving a geometric distribution.
Basketball player Shaquille O’Neal makes a free-throw show about 52.6% of the
time. Find the probability that the first shot O’Neal makes is the second shot
attempted.
From experience, you know that the probability that you will make a sale on any
given telephone call is 0.23. Find the probability that your first sale on any given
day will occur on your fourth or fifth sales call.
Find the probability that your first sale will occur before your fourth sales call.
If the probability experiment is binomial or geometric, then answer the question.
If not, then write “not binomial or geometric”.
In a recent year, Barry Bonds hit 73 home runs in the 153 games he played.
Assume that his home run production stayed at that level the following season.
What is the probability that he would hit his first home run on the first or second
game of the season?
It is estimated that sharks kill 10 people each year worldwide. What is the
probability that at least three people are killed by sharks this year?
One in four adults is currently on a diet. In a random sample of eight adults, what
is the probability that the number currently on a diet is at most two?