# Probability – Example (Marbles Drawn) Part 1 (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise | Summary and Q&A

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July 6, 2015
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Infinity Learn NEET
Probability – Example (Marbles Drawn) Part 1 (GMAT/GRE/CAT/Bank PO/SSC CGL) | Don't Memorise

## TL;DR

The video explains how to calculate the probability of drawing two red marbles from a box with three red and five blue marbles.

## Key Insights

• 🛻 Two scenarios for drawing two marbles: pick and pick without replacement, and pick replace pick.
• 🛻 In pick and pick without replacement, the second event depends on the outcome of the first event, while in pick replace pick, the two events are independent.
• 🛻 The probability of drawing a red marble in the pick and pick without replacement scenario is 3/8 for the first marble and 2/7 for the second marble.
• 🛻 Picking two marbles simultaneously is equivalent to the pick and pick without replacement scenario.

## Transcript

this box has three red marbles and five blue ones and two marbles are drawn at random yes two marbles are drawn from these eight what is the probability that both of them are R we have seen a similar example earlier pause the video and think about how you could approach this problem if you are confused then that's good because there are two possibi... Read More

### Q: What are the two scenarios for drawing two marbles?

The two scenarios are pick and pick without replacement, and pick replace pick. In the first scenario, the second event depends on the outcome of the first event, while in the second scenario, the two events are independent of each other.

### Q: What is the probability of drawing a red marble in the pick and pick without replacement scenario?

The probability of drawing a red marble in the pick and pick without replacement scenario is 3/8 for the first marble and 2/7 for the second marble.

### Q: Why do we multiply the probabilities in the pick and pick without replacement scenario?

We multiply the probabilities because the probability of A and B happening is equal to the probability of A multiplied by the probability of B given that A has already happened. In this case, picking a red marble and then picking another red marble.

### Q: Why is picking two marbles simultaneously the same as the pick and pick without replacement scenario?

Picking two marbles simultaneously may seem different, but the outcome is the same as picking two marbles one after the other. Therefore, the probability for both scenarios is the same.

## Summary & Key Takeaways

• The video discusses two scenarios for drawing two marbles: pick and pick without replacement, and pick replace pick.

• In both scenarios, the probability of drawing the first red marble is 3/8, and the probability of drawing the second red marble is either 2/7 or 3/8, depending on the scenario.

• The video also mentions that picking two marbles simultaneously is the same as the pick and pick without replacement scenario.