Question

Identify the option below that represents dependent events. Select the correct answer below: drawing a face card and then drawing a 3 without replacement from a standard deck of cards rolling a sum of 6 from the first two rolls of a standard die and a sum of 4 from the second two rolls drawing a 2 and drawing a 4 with replacement from a standard deck of cards drawing a heart and drawing another heart with replacement from a standard deck of cards.

Answer 1

First Option

Drawing a face card and then drawing a 3 without replacement.

Since we are drawing 3 without replacement, then it means the probability of drawing 3 will depend on the first event.

If in the first event, a face card is drawn, then the probability of drawing a 3 will be = 4/51 because there are 4 cards of 3, and since we are drawing it without replacing the first card in the deck so we have only 51 cards to choose from.

But if the first card is itself a 3, then the probability of drawing a 3 will be = 3/51 because a 3 has already been withdrawn from the deck.

So, we can see that the outcome of the first event influences the probability of the second event, hence these are dependent events.

Second Option

Rolling a sum of 6 from from the first 2 rolls and a sum of 4 from the second 2 rolls.

These are independent events since the outcome of a dice is totally independent of anything.

Third Option

Drawing a 2 and drawing a 4 from the deck of cards with replacement.

Since we are replacing the drawn card back to the deck hence the probability of drawing a 4 will always be 4/52 irrespective of the result of the first event.

So these are also independent events.

Fourth Option

Drawing a heart and drawing another heart with replacement from a deck of cards.

Here also, since we are replacing the chosen card back to the deck hence we have the probability of drawing hearts always = 13/52.

These are also independent events.

Answer - The first option has dependent events.

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