Question

10 different names are put into a computer and one of the names is Colin.

On Saturday the computer chooses two names at random.

The computer is set so that the same name can be chosen twice.

What is the probability that Colin is chosen at least once?

Answer 1

Probability that Colin is chosen at least once is 0.19.

Step-by-step explanation:

We are given that 10 different names are put into a computer and one of the names is Colin.

On Saturday the computer chooses two names at random.  The computer is set so that the same name can be chosen twice.

Let the Probability that chosen name is Colin =  $\frac{1}{10}$ = 0.1

So, Probability that chosen name is different from Colin = 1 - 0.1 = 0.9

Now, probability that Colin is chosen at least once = 1 - Probability that both names chosen is not of Colin

                           =  $1-(\frac{9}{10} \times \frac{9}{10} )$

                           =  $1-\frac{81}{100}$

                           =  $\frac{19}{100}$ = 0.19

Hence, probability that Colin is chosen at least once is 0.19.