Three cards are drawn with replacement from a standard deck. What is the probability that the first card will be a club, the second card will be a red card, and the third card will be an ace? Express your answer as a fraction or a decimal number rounded to four decimal places.
Think about how many of each there are in a deck of 52.
(1/4)(1/2)(1/13) = 1/104
To find the probability, we first need to determine the number of favorable outcomes and the number of possible outcomes.
There are 13 clubs in a standard deck of 52 cards, so the probability of drawing a club on the first card is 13/52.
After replacing the first card, there are 26 red cards remaining out of a total of 52 - 1 = 51 cards. Therefore, the probability of drawing a red card on the second draw is 26/51.
For the third draw, there are 4 aces remaining out of a total of 51 - 1 = 50 cards (since we have already drawn a card in the previous two steps). So the probability of drawing an ace on the third draw is 4/50.
Since each draw is independent, we multiply the probabilities together:
(13/52) * (26/51) * (4/50) = 0.0126
Hence, the probability that the first card will be a club, the second card will be a red card, and the third card will be an ace is 0.0126 (rounded to four decimal places).
To find the probability of drawing a club, a red card, and an ace in three consecutive draws with replacement, we need to calculate the individual probabilities of each event and multiply them together.
Step 1: Probability of drawing a club:
A standard deck of 52 cards contains 13 clubs. The probability of drawing a club on the first draw is 13/52 since there are 13 clubs out of 52 total cards.
Step 2: Probability of drawing a red card:
There are 26 red cards in a standard deck (13 hearts and 13 diamonds). Since we are drawing with replacement, the composition of the remaining deck does not change. Therefore, the probability of drawing a red card on the second draw is still 26/52.
Step 3: Probability of drawing an ace:
A standard deck contains four aces. Since we are drawing with replacement, the probability of drawing an ace on the third draw is 4/52.
Step 4: Multiply the probabilities together:
To find the overall probability, we multiply the three individual probabilities calculated above:
(13/52) * (26/52) * (4/52) = 0.0239
Therefore, the probability of drawing a club on the first draw, a red card on the second draw, and an ace on the third draw is approximately 0.0239, rounded to four decimal places.