Question

A teacher has a box of crayons that contains 6

red, 6 blue, 6 green and 6 purple crayons.


Heather picks a crayon out of the box and does


not replace it. She then picks a second crayon.


What is the probability that the first crayon is


purple and the second crayon is purple?

Answer 1

`(1)/(23)`

Explanation:

Given: A box of crayons that contains 6 red, 6 blue, 6 green and 6 purple crayons.

To find: probability that the first crayon is purple and the second crayon is purple if she picks a crayon out of the box and does not replace it and then picks a second crayon.

Solution:

Probability refers to chances of occurrence of an event.

Let A denotes event that the first crayon drawn by her is purple and B denotes event that the second crayon drawn by her is purple.

These events are dependent.

Using multiplication rule of probability,

probability that the first crayon is purple and the second crayon is purple if she picks a crayon out of the box and does not replace it and then picks a second crayon =
`P(A)P(B|A)`

P(A) = number of purple crayons/Total number of crayons =
`(6)/(6+6+6+6)=(6)/(24)=(1)/(4)`

P(B|A) =
`(6-1)/(24-1)=(5)/(23)`

So,

probability that the first crayon is purple and the second crayon is purple if she picks a crayon out of the box and does not replace it and then picks a second crayon =
`(1)/(5)((5)/(23))=(1)/(23)`