Question

For each of the following situations, determine whether the given random variable has a binomial distribution. Justify your answer.

1. Shuffle a deck of cards. Turn over the top card. Put the card back in the deck, and shuffle again. Repeat this process 10 times.

Let $X=$the number of aces you observe.

Short answer

Yes, the given statement is a binomial distribution.

Step-by-step solution

Given Information

Given in the question that, we have to shuffle a deck of cards. Turn over the top card. Put the card back in the deck, and shuffle again. Repeat this process 10 times.

$X=$Number of aces you observe.

Explanation

A single trial does not influence the outcome of any other trial since the cards are replaced and shuffled each time.

In advance, $10$trials are set.

The probability of success is $\frac{4}{52}$for each trial.

It is a binomial setting.

This is a binomial random variable since $X$counts the number of successes, $n=10$and $p=\left(\frac{4}{52}\right)$