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A box contains 5 white and 3 black balls. If one ball is drawn and it is black,

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Question: A box contains 5 white and 3 black balls. If one ball is drawn and it is black, what is the probability that the next ball drawn is white?

Options:

  1. 5/7
  2. 3/8
  3. 5/8
  4. 1/2

Correct Answer: 5/7

Solution: 

After drawing a black ball, there are 5 white and 2 black balls left. The probability of drawing a white ball next is 5/7.

A box contains 5 white and 3 black balls. If one ball is drawn and it is black,

Practice Questions

Q1
A box contains 5 white and 3 black balls. If one ball is drawn and it is black, what is the probability that the next ball drawn is white?
  1. 5/7
  2. 3/8
  3. 5/8
  4. 1/2

Questions & Step-by-Step Solutions

A box contains 5 white and 3 black balls. If one ball is drawn and it is black, what is the probability that the next ball drawn is white?
Correct Answer: 5/7
  • Step 1: Start with the total number of balls in the box. There are 5 white balls and 3 black balls, making a total of 8 balls.
  • Step 2: One ball is drawn and it is black. This means we have removed 1 black ball from the box.
  • Step 3: After removing the black ball, count the remaining balls. There are still 5 white balls and now only 2 black balls left.
  • Step 4: Now, calculate the total number of balls left in the box. There are 5 white + 2 black = 7 balls remaining.
  • Step 5: To find the probability of drawing a white ball next, use the formula: Probability = (Number of favorable outcomes) / (Total number of outcomes).
  • Step 6: The number of favorable outcomes (drawing a white ball) is 5, and the total number of outcomes (total balls left) is 7.
  • Step 7: Therefore, the probability of drawing a white ball next is 5/7.
  • Conditional Probability – The probability of an event occurring given that another event has already occurred.
  • Counting Principles – Understanding how to count the remaining outcomes after an event has taken place.
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