A box contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is black given that it is not white?
Practice Questions
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Q1
A box contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is black given that it is not white?
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The total number of balls is 10. The number of favorable outcomes (black balls) is 6. The probability that the ball is black given that it is not white is P(Black | Not White) = 6/6 = 1.
Questions & Step-by-step Solutions
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Q
Q: A box contains 4 white and 6 black balls. If one ball is drawn at random, what is the probability that it is black given that it is not white?
Solution: The total number of balls is 10. The number of favorable outcomes (black balls) is 6. The probability that the ball is black given that it is not white is P(Black | Not White) = 6/6 = 1.
Steps: 6
Step 1: Identify the total number of balls in the box. There are 4 white balls and 6 black balls, so the total is 4 + 6 = 10 balls.
Step 2: Determine the condition given in the question. We need to find the probability of drawing a black ball given that the ball drawn is not white.
Step 3: Since we are only considering the balls that are not white, we only look at the black balls. There are 6 black balls.
Step 4: Count the total number of balls that are not white. Since there are 4 white balls, the remaining balls (which are not white) are the 6 black balls.
Step 5: Calculate the probability. The probability of drawing a black ball given that it is not white is the number of black balls divided by the total number of balls that are not white. This is 6 (black balls) / 6 (total not white) = 1.
Step 6: Conclude that the probability of drawing a black ball given that it is not white is 1.
