two cards are drawn without replacement from a shuffled deck of 52 cards.
determine the probability of each event:
a) the first card is a heart and the second is the queen of hearts
b) the first card is the queen of hearts and the second is a heart
Pr(h,qh)=1-pr(nohearts, not qhearts)= 1-(39/52)(50/51)
Pr(qH,h)=(1/52)(12/51)
check my thinking
To determine the probabilities of the events, we'll start by calculating the total number of possible outcomes and then divide it by the sample space.
a) The first card is a heart and the second is the queen of hearts:
Step 1: Calculate the total number of possible outcomes: There are 52 cards in the deck, and after drawing the first card, there are 51 cards left.
Step 2: Calculate the number of favorable outcomes: There are 13 hearts in the deck, and after drawing the first heart, there are 12 hearts left. Additionally, we need to draw the queen of hearts, which is only one card.
Step 3: Calculate the probability: Divide the number of favorable outcomes by the total number of possible outcomes.
Total number of possible outcomes = 52 * 51 = 2652
Number of favorable outcomes = 13 * 12 * 1 = 156
Probability = 156 / 2652 = 1 / 17
Therefore, the probability of drawing a heart as the first card and the queen of hearts as the second card is 1/17.
b) The first card is the queen of hearts and the second is a heart:
Step 1: Calculate the total number of possible outcomes: There are 52 cards in the deck, and after drawing the first card, there are 51 cards left.
Step 2: Calculate the number of favorable outcomes: We need to draw the queen of hearts as the first card, which is only one card. Afterward, there are 13 hearts left in the deck.
Step 3: Calculate the probability: Divide the number of favorable outcomes by the total number of possible outcomes.
Total number of possible outcomes = 52 * 51 = 2652
Number of favorable outcomes = 1 * 13 = 13
Probability = 13 / 2652 = 1 / 204
Therefore, the probability of drawing the queen of hearts as the first card and a heart as the second card is 1/204.