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A box contains 5 red, 3 green, and 2 blue marbles. If a marble is drawn and it i

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Question: A box contains 5 red, 3 green, and 2 blue marbles. If a marble is drawn and it is known to be red, what is the probability that it is the first marble drawn?

Options:

  1. 1/5
  2. 1/3
  3. 1/2
  4. 1/10

Correct Answer: 1/5

Solution: 

The probability of drawing a red marble is independent of the order. Therefore, P(First | Red) = 1/5.

A box contains 5 red, 3 green, and 2 blue marbles. If a marble is drawn and it i

Practice Questions

Q1
A box contains 5 red, 3 green, and 2 blue marbles. If a marble is drawn and it is known to be red, what is the probability that it is the first marble drawn?
  1. 1/5
  2. 1/3
  3. 1/2
  4. 1/10

Questions & Step-by-Step Solutions

A box contains 5 red, 3 green, and 2 blue marbles. If a marble is drawn and it is known to be red, what is the probability that it is the first marble drawn?
  • Step 1: Understand that there are 5 red marbles in the box.
  • Step 2: Recognize that the total number of marbles is 5 red + 3 green + 2 blue = 10 marbles.
  • Step 3: When we know a marble drawn is red, we are only considering the red marbles.
  • Step 4: The question asks for the probability that the red marble drawn is the first one drawn.
  • Step 5: Realize that the order of drawing does not affect the probability of it being red.
  • Step 6: Since there are 5 red marbles, the probability of drawing any one of them first is 1 out of 5.
  • Step 7: Therefore, the probability that the red marble drawn is the first one is 1/5.
  • Conditional Probability – The probability of an event occurring given that another event has already occurred.
  • Independence of Events – Understanding that the probability of one event does not affect the probability of another event.
  • Total Probability – The total number of outcomes and how they relate to the specific event in question.
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