A box has 6 red balls and 4 white balls. A ball is picked at random and replaced in the box, after which a second ball is picked. The probability of both the balls being red, rounded to 2 decimal places, is ____.Correct answer is '0.36'. Can you explain this answer?

Question

Answer

Probability of picking a red ball in the first draw
- The box has a total of 6 red balls and 4 white balls.
- Therefore, the probability of picking a red ball in the first draw is 6/10 or 0.6.

Probability of picking a red ball in the second draw
- Since the first ball is replaced back into the box, the total number of balls in the box remains the same.
- Hence, the probability of picking a red ball in the second draw is also 6/10 or 0.6.

Probability of both balls being red
- To find the probability of both balls being red, we need to multiply the probabilities of the individual events.
- Therefore, the probability of both balls being red is 0.6 * 0.6 = 0.36.

Explanation
- The probability of picking a red ball in the first draw is 0.6 because out of the total 10 balls, 6 are red.
- Since the first ball is replaced back into the box, the probability of picking a red ball in the second draw remains the same at 0.6.
- To find the probability of both balls being red, we multiply the probabilities of the individual events. This is because the two events are independent, meaning that the outcome of the first event does not affect the outcome of the second event.
- Therefore, the probability of both balls being red is 0.6 * 0.6 = 0.36 or 36%.

Conclusion
- The probability of both balls being red, when one ball is picked at random and replaced in the box before picking the second ball, is 0.36 or 36%.

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