Question

A bag contains 26 tiles letters a through z find the probability of drawing two vowels with replacement find the probability of drawing two vowels without replacement round the answers to the nearest thousandths which event is independent which event is dependent

Answer 1

With replacement, 0.037, independent

Without replacement, 0.031, dependent

Explanation:

There are 5 vowels (not including y).

The probability the first letter is a vowel is 5/26.

With replacement, the probability the second letter is a vowel is also 5/26.

The total probability is (5/26) (5/26) = 0.037.

Since the first letter is replaced, the probability of the second letter is not affected, so the events are independent.

Without replacement, the probability the second letter is a vowel is 4/25.

The total probability is (5/26) (4/25) = 0.031.

Since the first letter is not replaced, the probability of the second letter is affected, so the events are dependent.