Probability – Example (Marbles Drawn) Part 2 (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise

TL;DR

Calculate the probability of drawing two marbles of the same color from a box containing red and blue marbles.

Transcript

this box contains three red marbles and five blue ones and two marbles are drawn from it what is the probability that both are of the same color as we saw in the previous part of the session there will be two cases here here's the first one we pick a marble and then pick another one and in the second case we pick a marble put it back in and then pi... Read More

Key Insights

• 🛻 There are two cases when calculating the probability of drawing marbles of the same color: pick and pick without replacement, and pick and put back.
• 😪 The probability of drawing two marbles of the same color can be found by summing the individual probabilities of drawing two red marbles and two blue marbles.
• 📪 The probability is calculated based on the number of red and blue marbles in the box, and the chosen case for picking the marbles.

Questions & Answers

Q: How do you calculate the probability of drawing two marbles of the same color from a box?

There are two cases: pick and pick without replacement. In the pick and pick case, calculate the probability of picking two red marbles as (3/8) * (2/7), and two blue marbles as (5/8) * (4/7). In the pick and put back case, the probability of two red marbles is (3/8) * (3/8), and two blue marbles is (5/8) * (5/8).

Q: What if I want to know the probability of drawing two marbles of different colors?

To find the probability of drawing two different color marbles, there are two cases: red first and blue second, or blue first and red second. Calculate the probability as (3/8) * (5/7) + (5/8) * (3/7).

Q: What is the difference between the pick and pick case and the pick and put back case?

In the pick and pick case, the marble is not replaced after it is drawn, so the probability for the second marble changes. In the pick and put back case, the marble is replaced before picking the second one, so the probability for the second marble remains the same.

Q: How does the number of marbles in the box affect the probability?

The number of marbles in the box affects the probability calculations. If the number of red and blue marbles changes, the probabilities for each case will also change accordingly.

Summary & Key Takeaways

• The content explains how to calculate the probability of drawing two marbles of the same color from a box of three red and five blue marbles.

• There are two cases: pick and pick without replacement. In the first case, the probability of drawing two red marbles is (3/8) * (2/7), and the probability of drawing two blue marbles is (5/8) * (4/7). In the second case, the probability of two red marbles is (3/8) * (3/8), and the probability of two blue marbles is (5/8) * (5/8).

• If the question asks for the probability of drawing two different color marbles, the probabilities are calculated similarly and summed up: (3/8) * (5/7) + (5/8) * (3/7).