A state lottery randomly chooses 7 balls numbered from 1-36 without replacement.
ID: 3040059 • Letter: A
Question
A state lottery randomly chooses 7 balls numbered from 1-36 without replacement. You choose 7 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 success, specify the values n, p, and q and list the possible values of the random variable x. A state lottery randomly chooses 7 balls numbered from 1-36 without replacement. You choose 7 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 success, specify the values n, p, and q and list the possible values of the random variable x.Explanation / Answer
After the state has chosen 7 balls, we can consider two different groups of numbers, one where the number is such that the ball corresponding to that that number has been selected in the state lottery and second if the number is such that the ball corresponding to that number has not been selected by the state lottery.
Let the random variable x represent the number of numbers among the 7 numbers we have chosen which match the numbers from the numbers corresponding to the balls which have ben selected in state lottery.
There are 7 favorable outcomes out of 36 total outcomes.The event will be a success if the number we have chosen is among the 7 which are chose by the state lottery. Since it has been not specified that while choosing 7 numbers we cannot select a number twice, the probability of each number selection would be independent of each other satisfying the second condition of binomial distribution. The first condition was that there will be only two outcomes.
Thus the given experiment is a binomial. The number of trials is 7.
n = 7
The probability of success in single trial would be given by,
p = 7/36
The probability of failure in a single trial would be given by,
q = (36-7)/36 = 29/36
x can take any integer values from 0 to 7.
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