three(3) cards are drawn from a deck of playing cards.find the probability that the first card is red,the second card is a black king,and the third card is a black king
prob = (26/52)(2/51)(1/50) = 1/2550
To find the probability that the first card is red, the second card is a black king, and the third card is a black king, we need to consider the total number of favorable outcomes and the total number of possible outcomes.
Step 1: Determine the number of favorable outcomes.
The first card being red means it can be any of the 26 red cards in the deck.
After the first card is drawn, there are 51 cards remaining in the deck. The probability of drawing a black king as the second card is 2/51 because there are two black kings remaining out of 51 cards.
The third card also needs to be a black king, which means there is only one remaining black king out of the 50 cards left in the deck.
So, the number of favorable outcomes is:
26 (red cards) x 2 (black kings) x 1 (black king) = 52.
Step 2: Determine the number of possible outcomes.
To calculate the number of possible outcomes, consider that 3 cards are being drawn from a standard deck of 52 cards without replacement. This means that each card drawn changes the number of cards remaining. The number of possible outcomes for the first card is 52 (since any card can be selected), for the second card it is 51 (one card has already been drawn), and for the third card it is 50 (two cards have already been drawn).
So, the number of possible outcomes is:
52 (first card) x 51 (second card) x 50 (third card) = 132,600.
Step 3: Calculate the probability.
Now that we have the number of favorable outcomes and the number of possible outcomes, we can calculate the probability using the formula:
Probability = Number of favorable outcomes / Number of possible outcomes
Probability = 52 / 132,600
Simplifying this fraction, we get:
Probability = 1 / 2,550
Thus, the probability that the first card is red, the second card is a black king, and the third card is a black king is 1/2,550.