The probability of drawing two aces from a standard deck is 0.0059. We know this probability, but we don't know if the first card was replaced. If the two draws are defined as event A and event B, are the events dependent or independent?

Question

Mathematics

Jayden Walton

7 August, 14:37

The probability of drawing two aces from a standard deck is 0.0059. We know this probability, but we don't know if the first card was replaced. If the two draws are defined as event A and event B, are the events dependent or independent?

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Answers (1)

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Emmy Berry · Answer 1

To answer the question we need to know if we replaced or not.

Lets calculate the 2 probabilities.

1, No replacement

first draw is an ace P=4/52

2nd draw is an ace P=3/51

Both are A: P=4/52 * 3/51 = 0,0045

2, With replacement

Both draws P=4/52

Both A: P = (4/52) ^2 = 0,0059

So we know that it was with replacement.

This means theat the two events are independent. (both draws have 4/52 chance, not affecting eachother)