A box contains 3 black balls, 2 red balls, and 5 white balls. One ball is drawn, it is not replaced, and a second ball is drawn. Find the probability that the first ball is red and the second is black
Question
A box contains 3 black balls, 2 red balls, and 5 white balls. One ball is drawn, it is not replaced, and a second ball is drawn. Find the probability that the first ball is red and the second is black
Solution
Sure, here is the step by step solution:
Step 1: Calculate the total number of balls. The total number of balls is 3 (black) + 2 (red) + 5 (white) = 10 balls.
Step 2: Calculate the probability of drawing a red ball first. The probability of drawing a red ball first is the number of red balls divided by the total number of balls. So, the probability is 2 (red balls) / 10 (total balls) = 0.2.
Step 3: Calculate the total number of balls left after one is drawn. After drawing one ball, the total number of balls left is 10 - 1 = 9 balls.
Step 4: Calculate the probability of drawing a black ball second. The probability of drawing a black ball second is the number of black balls divided by the total number of balls left. So, the probability is 3 (black balls) / 9 (total balls left) = 0.333.
Step 5: Calculate the total probability. The total probability of drawing a red ball first and a black ball second is the product of the two individual probabilities. So, the total probability is 0.2 * 0.333 = 0.0666.
So, the probability that the first ball is red and the second is black is 0.0666.
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