Question

an urn contains 6 yellow,5 blue and 2 white marbles. if three marbles are picked at random, what is the probability at least one is blue?

Answer 1

Answer:

The required probability is 115/143.

Step-by-step explanation:

The probability that at least one is blue= 1- Probability that none is blue

Let the probability of not picking up any blue marble is P

P= Event/Total outcomes

Here, total outcomes are 13C3 ( Picking up three marbles out of a total of 13 marbles)

P= 8C3/ 13C3 ( Leaving out the blue marbles we have 6 red marbles and 2 white marbles, out of which 3 need to be selected)

Now finding out the value of 8C3 = 8!/(3! * 5!)

So, 8C3 = (8*7*6) /( 3*2) = 336/6 = 56

Now finding out the value of 13C3 = 13!/ (3! *10!)

So, 13C3 =( 13*12*11)/ (3*2) = 286

Hence, the required probability P = 56/286 = 28/143

So, the probability that at least one is blue = 1-28/143 = 115/143