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A state lottery randomly chooses 8 balls numbered from 1 through 39 without replacement. You choose...

A state lottery randomly chooses 8 balls numbered from 1 through 39 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.

Math   Statistics-And-Probability   
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Answer #1

Replacement is not allowed.

Number of trials n = 8 (fixed). This condition is satisfied.

Trials are dependent because the selection of first ball affect the selection of second ball. This condition is not satisfied.

Two possible outcomes, i.e. probability of matched number and probability of non matched number. This condition is satisfied.

Equal probability on each trials is not satisfied in this because the replacement is not allowed, which means probability of success on each trial is different from previous trial. This condition is not satisfied.

Hence, two of the four conditions for binomial are not satisfied. So, it is not a binomial

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