A box contains 10 red marbles and 10 green marbles. Sampling at random from the box five times with replacement, you have drawn a red marble all five times. What is the probability of drawing a red marble the sixth time?

Explanation:

Since the sampling at random from the box containing the marbles is with replacement, that is, after picking a marble, it is replaced before picking another one, the probability of picking a red marble is the same for each sampling. Probability, P(A) is given by the ratio of the number of favourable outcome to the total number of favourable outcome.

From the question,

Number of favourable outcome = number of red marbles =10

Total number of favourable outcome = total number of marbles = 10+10= 20

Hence, probability of drawing a red marble P(R) = 10 ÷ 20

P(R) = 1/2

Since the probability of picking a red marble is the same for each sampling, the probability of picking a red marble the sixth time is 1/2

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