Question

Caleb is selecting cards from a set of 12 cards numbered 1-2-4-4-5-5-5-5-6-9-10-13.

What is the probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the card, and then draws a 5 on the second selection? Express your answer as a fraction in lowest terms.

Answer 1

The probability that Caleb selects a 5 on the first selection, returns the card to the deck, shuffles the cards, and then draws a 5 on the second selection is 1/36.

Step-by-step explanation:

To calculate the probability of Caleb selecting a 5 on the first selection, returning the card to the deck, shuffling the cards, and then drawing a 5 on the second selection, we need to determine the number of favorable outcomes and the total number of possible outcomes.

There are 12 cards in total, and since Caleb selects the first card and returns it to the deck, the total number of outcomes for the first selection is 12. The probability of selecting a 5 on the first selection is 4/12, as there are 4 cards with a value of 5.

After shuffling the cards, Caleb has 12 cards to choose from for the second selection. There is still 1 card with a value of 5 in the deck, so the probability of selecting a 5 on the second selection is 1/12.

To find the overall probability, we multiply the probabilities of each selection: (4/12) * (1/12) = 1/36.