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A box contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random,

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Question: A box contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue given that it is not red?

Options:

  1. 1/2
  2. 1/4
  3. 1/3
  4. 1/5

Correct Answer: 1/3

Solution: 

The total number of balls that are not red is 5 (3 blue + 2 green). The probability that the ball is blue given it is not red is P(Blue | Not Red) = 3/5.

A box contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random,

Practice Questions

Q1
A box contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue given that it is not red?
  1. 1/2
  2. 1/4
  3. 1/3
  4. 1/5

Questions & Step-by-Step Solutions

A box contains 5 red, 3 blue, and 2 green balls. If one ball is drawn at random, what is the probability that it is blue given that it is not red?
Correct Answer: 3/5
  • Step 1: Count the total number of balls in the box. There are 5 red, 3 blue, and 2 green balls.
  • Step 2: Calculate the total number of balls: 5 (red) + 3 (blue) + 2 (green) = 10 balls.
  • Step 3: Identify the balls that are not red. These are the 3 blue and 2 green balls.
  • Step 4: Count the number of balls that are not red: 3 (blue) + 2 (green) = 5 balls.
  • Step 5: Determine how many of the non-red balls are blue. There are 3 blue balls.
  • Step 6: Calculate the probability of drawing a blue ball given that it is not red. This is the number of blue balls divided by the total number of non-red balls: 3 (blue) / 5 (not red) = 3/5.
  • Step 7: Write the final answer: The probability that the ball is blue given that it is not red is 3/5.
  • Conditional Probability – The probability of an event occurring given that another event has already occurred.
  • Total Probability – Understanding the total number of outcomes relevant to the condition specified.
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