A state lottery randomly chooses 8 balls numbered from 1 through 41 without replacement. You choose 8 numbers and purchase a lottery ticket.
The random variable represents the number of matches on your ticket to the numbers drawn in the lottery. Determine whether this experiment is binomial. If so, identify a success, specify the values n, p, and q and list the possible values of the random variable x.
1. Is the experiment binomial?
A. No, there are more than two outcomes for each trial.
B. No, because the probability of success is different for each trial.
C. Yes, the probability of success is the same for each trial.
D. Yes, there are a fixed number of trials and the trials are independent of each other.
2. Identify a success. Choose the correct answer below.
A. A success is matching one of the numbers in the lottery.
B. A success is matching all of the numbers in the lottery.
C. A success is the number of matches on your ticket to the numbers drawn in the lottery.
D. The experiment is not binomial.
Answer and Explanation:
1) A state lottery randomly chooses 8 balls numbered from 1 through 41 without replacement. Following are some conditions of binomial distribution:
a) Fixed number of Trials:
It is given that, number of trials, n=8. Therefore, n is finite, positive and having integral value. Condition (a) is satisfied.
b) Independent Trials:
Since balls are chosen without any replacement which results in dependency of the second ball on the first. Therefore, trials are not independent. Condition (b) is not satisfied.
c) Probability of Success:
Since 8 balls are chosen randomly without replacement, the probability of success is not the same on every trial. Therefore, Condition (c) is not satisfied.
Hence, the experiment is not binomial.
2) We define success as, all the numbers is matching with the ticket and Failure as, if there is no match with the ticket. Therefore Option (B) is correct.
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from Algebra II TextbookChapter 21 / Lesson 16