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A box contains 5 red, 3 green, and 2 blue marbles. If one marble is drawn at ran

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

Options:

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

Correct Answer: 1/3

Solution: 

The total number of non-red marbles is 5 (3 green + 2 blue). The probability that the marble is green given that it is not red is P(Green | Not Red) = 3/5.

A box contains 5 red, 3 green, and 2 blue marbles. If one marble is drawn at ran

Practice Questions

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

Questions & Step-by-Step Solutions

A box contains 5 red, 3 green, and 2 blue marbles. If one marble is drawn at random, what is the probability that it is green given that it is not red?
  • Step 1: Count the total number of marbles in the box. There are 5 red, 3 green, and 2 blue marbles.
  • Step 2: Calculate the total number of non-red marbles. This is done by adding the number of green and blue marbles: 3 green + 2 blue = 5 non-red marbles.
  • Step 3: Identify how many of the non-red marbles are green. There are 3 green marbles.
  • Step 4: Calculate the probability of drawing a green marble given that it is not red. This is done by dividing the number of green marbles by the total number of non-red marbles: 3 green / 5 non-red = 3/5.
  • Step 5: State the final answer: The probability that the marble is green 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 how to calculate the total number of favorable outcomes versus the total number of possible outcomes.
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