what is the probability of selecting an eight followed by a nine from a deck of 52 cards if the first card is replaced before second is drawn?
please help me.
To calculate the probability of selecting an eight followed by a nine from a deck of 52 cards, assuming the first card is replaced before the second is drawn, you need to consider the total number of possible outcomes and the number of favorable outcomes.
First, let's determine the total number of possible outcomes. In a deck of 52 cards, there are 4 eights and 4 nines, so a total of 8 cards that fulfill the conditions for the desired outcome.
Next, let's calculate the number of favorable outcomes:
To have an eight followed by a nine, we need to choose an eight as the first card and a nine as the second card. Since the first card is replaced before drawing the second card, the probability of drawing an eight and a nine in two separate draws is the product of their individual probabilities.
The probability of drawing an eight from the deck is 4/52, as there are 4 eights out of the 52 cards.
The probability of drawing a nine from the deck is also 4/52 since there are 4 nines out of the 52 cards.
To get the probability of both events occurring, we multiply these probabilities together:
P(8 and 9) = P(8) * P(9) = (4/52) * (4/52) = 1/169
So, the probability of selecting an eight followed by a nine, with replacement, from a deck of 52 cards is 1/169.