Question

Two cards are chosen at random from a deck of cards. What is the probability of selecting a number card (2, 3, 4, 5, 6, 7, 8, 9 or 10) followed by an ace with replacement? Is this a independent or dependent scenario

Answer 1

The probability of selecting a number card (2, 3, 4, 5, 6, 7, 8, 9, or 10) followed by an ace with replacement is 9/169. This is an independent scenario.

Step-by-step explanation:

The probability of selecting a number card (2, 3, 4, 5, 6, 7, 8, 9, or 10) followed by an ace with replacement can be calculated as follows:

Step 1: Determine the probability of selecting a number card. There are 36 number cards in a deck (9 number cards in each suit), and there are 52 cards in total. Therefore, the probability of selecting a number card is 36/52 or 9/13.

Step 2: Determine the probability of selecting an ace. There are 4 aces in a deck (1 ace in each suit). Therefore, the probability of selecting an ace is 4/52 or 1/13.

Step 3: Since the events are independent (you put each card back before picking the next one), multiply the probabilities from Step 1 and Step 2 to find the probability of both events occurring. The probability of selecting a number card followed by an ace with replacement is (9/13) * (1/13) = 9/169.

Therefore, the probability of selecting a number card followed by an ace with replacement is 9/169. This is an independent scenario.