Concept explainers
Using set notation, write out the
a. A coin is tossed three times in a row. The observation is how the coin lands (H or T ) on each toss.
b. A basketball player shoots three consecutive free throws. The observation is the result of each free throw (
c. A coin is tossed three times in a row. The observation is the number of times the coin comes up tails.
d. A basketball player shoots three consecutive free throws. The observation is the number of successes.
(a)
To calculate:
The Sample Space for a coin tossed three times.
Answer to Problem 1E
Solution:
The sample space is
Explanation of Solution
Procedure used:
When a coin is tossed three times, the outcome in each toss is either head
There is one way to get 3 heads:
There are 3 ways to get 2 heads:
There is 1 way to get 3 tails:
There are 3 ways to get 1 head:
The Sample Space of a sequence of three fair coin tosses is all
So there are 8 events in the sample space. If the coin tossed is fair than each event is equally possible.
Given:
A coin is given for tossing.
Conclusion:
Thus, the sample space is
(b)
To calculate:
The Sample Space for three throws of basketball.
Answer to Problem 1E
Solution:
The Sample Space of a sequence of three consecutive free throws is
Explanation of Solution
Given:
A basketball player shoots three consecutive free throws.
Calculation:
The outcome in each throw is either success
There is one way to get 3 successes:
There are 3 ways to get 2 successes:
There is 1 way to get 3 failures:
There are 3 ways to get 1 success:
The Sample Space of a sequence of three consecutive free throws is all
So there are 8 events in the sample space.
Conclusion:
Thus, the Sample Space of a sequence of three consecutive free throws is
(c)
To calculate:
The Sample Space for number of times the coin comes up a tail.
Answer to Problem 1E
Solution:
The Sample Space of the number of times the coin comes up tails is,
Explanation of Solution
Given:
A coin is given for tossing.
Calculation:
When a coin is tossed three times, the outcome in each toss is either head
Numbers of ways to get tail are:
No tail, one tail, two tails, and three tails in a sequence of three fair coin.
The Sample Space of the number of times the coin comes up tails is,
Conclusion:
Thus, the Sample Space of the number of times the coin comes up tails is,
(d)
To calculate:
The Sample Space of the number of times the free throw results in success.
Answer to Problem 1E
Solution:
The Sample Space of the number of times the free throw results in success is,
Explanation of Solution
Given:
A coin is given for tossing.
Calculation:
When a ball is thrown three times, the outcome in each throw is either success
Numbers of ways to get success:
No free throw results in success, one success, two successes, and three successes in a sequence of three free throws.
The Sample Space of the number of times the free throw results in success is,
Conclusion:
Thus, the Sample Space of the number of times the free throw results in success is,
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