You draw two card from a standard deck of 52 cards and replace the first one before drawing the second. Find the probablity of drawing a 4 for the frist card and a 9 for the second card
Prob. of 4 = 4/52 = 1/13
Prob. of 9 = 4/52 = 1/13
Probability of both events occurring is found by multiplying the individual probabilities.
To find the probability of drawing a 4 for the first card and a 9 for the second card, we need to break the problem down into two independent events: drawing a 4 on the first card and drawing a 9 on the second card.
1. Probability of drawing a 4 on the first card:
Since there is only one 4 in a standard deck of 52 cards, the probability of drawing a 4 on the first card is 1 out of 52. Therefore, the probability is 1/52.
2. Probability of drawing a 9 on the second card:
After replacing the first card back into the deck, we still have a standard deck of 52 cards for the second draw. However, this time we want to determine the probability of drawing a 9, which is also one card out of the 52-card deck. So, the probability of drawing a 9 on the second card is also 1/52.
Since we are replacing the first card before drawing the second one, these two events are independent, meaning that the outcome of the first draw does not affect the outcome of the second draw.
To find the combined probability of these two independent events occurring, we multiply their probabilities together:
P(drawing 4 for the first card and 9 for the second card) = P(drawing 4 on first card) * P(drawing 9 on second card)
Therefore, the probability of drawing a 4 for the first card and a 9 for the second card is (1/52) * (1/52) = 1/2704.
So, the probability is 1 out of 2704, or expressed as a fraction, 1/2704.