Question

Sonia has 5 yellow hair clips, 2 red hair clips and 3 blue hair clips. What is the probability she was picks a yellow hair clip and a blue hair clip without replacement?

Answer 1

The probability that Sonia picks a yellow hair clip and a blue hair clip without replacement =
`(1)/(6)`

Explanation:

Given:

Sonia has:

5 yellow hair clips

2 red hair clips

3 blue hair clips

To find the probability that she picks a yellow hair clip and a blue hair clip without replacement.

Solution:

Total number of clips =
`5+2+3` = 10

The probability that Sonia picks a yellow clip from the lot will be :

⇒
`\frac{\textrm{Number of yellow clips}}{\textrm{Total number of clips}}`

⇒
`(5)/(10)`

Simplifying fraction by dividing both numbers by their G.C.F.

⇒
`(5/ 5)/(10/ 5)`

⇒
`(1)/(2)`

Since no replacement is taking place, so after picking a yellow clip from the lot, the number of clips is decreased by 1.

So, new number of clips =
`10-1` = 9

The probability that Sonia picks a blue clip from the remaining lot will be :

⇒
`\frac{\textrm{Number of blue clips}}{\textrm{Total number of clips}}`

⇒
`(3)/(9)`

Simplifying fraction by dividing both numbers by their G.C.F.

⇒
`(3/ 3)/(9/ 3)`

⇒
`(1)/(3)`

The probability that she picks a yellow hair clip and a blue hair clip without replacement can be given as:

⇒
`(1)/(2)* (1)/(3)`

⇒
`(1* 1)/(2* 3)`

⇒
`(1)/(6)` (Answer)