Question 63

A bag contains 6 blue, 4 red, 3 yellow and 2 green marbles. If 4 marbles are picked up at random, what is the probability that atleast one of them is red?

Solution

Given that the total number of marbles is 15 and we have to select 4 of them

Probability of Selecting atleast one red marble = 1 - Probability of selecting no red marble

P(No red marble) = $$\dfrac{^{11}C_4}{^{15}C_4}=\dfrac{330}{1365}$$

So, P(Atleast one red marble) = $$1-\dfrac{330}{1365}=\dfrac{1035}{1365}=\dfrac{69}{91}$$

Hence, the answer is $$\dfrac{69}{91}$$

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