Question

Laura and Andy are trying out for a part in a school play. There is a total of 15 students trying out for the same part. If the students are chosen at random to audition, what is the probability that Laura will go first and Andy second?

Answer 1

The probability that Laura will go first and Andy second is
`((1)/(210) )`

Explanation:

The total number of students = 15

Out of the these, two students are Laura and Andy.

Let E: Event of choosing a random student for the part of school play.

Now, P(Choosing Laura first) =
`\frac{\textrm{The number of favorable student}}{\textrm{Total students}} = (1)/(15)`

Now, when Laura is chosen, the number of students left = 14

P(Choosing Andy second) =
`\frac{\textrm{The number of favorable student}}{\textrm{Total students}} = (1)/(14)`

⇒The combined probability of choosing Laura first and Andy second

=
`((1)/(15) )* ((1)/(14) ) = (1)/(210)`

Hence, the probability that Laura will go first and Andy second is
`((1)/(210) )`