Question

when drawing two cards without replacement from a standard deck of 52 cards, how many number of ways to obtain a king on the first draw and a heart on the second can be calculated separately for each draw.

Answer 1

To calculate the number of ways to obtain a king on the first draw and a heart on the second draw without replacement, we need to consider two separate events. The probability of drawing a king on the first draw is 4/52. After drawing a king on the first draw, the probability of drawing a heart on the second draw is 12/51. Multiplying these probabilities together gives an overall probability of 1/221.

Step-by-step explanation:

To calculate the number of ways to obtain a king on the first draw and a heart on the second draw without replacement, we need to consider two separate events.

1. King on the first draw: There are 4 kings in a standard deck of 52 cards, so the probability of drawing a king on the first draw is 4/52.
2. Heart on the second draw: After drawing a king on the first draw, there are now 51 cards remaining in the deck, with 12 hearts. So, the probability of drawing a heart on the second draw is 12/51.

Since these are separate events, we can multiply the probabilities together to find the overall probability: (4/52) * (12/51) = 1/221.