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

Answer:

The probability that Sonia picks a yellow hair clip and a blue hair clip without replacement = $\frac{1}{6}$

Step-by-step 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 :

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

⇒ $\frac{5}{10}$

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

⇒ $\frac{5\div 5}{10\div 5}$

⇒ $\frac{1}{2}$

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 :

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

⇒ $\frac{3}{9}$

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

⇒ $\frac{3\div 3}{9\div 3}$

⇒ $\frac{1}{3}$

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

⇒ $\frac{1}{2}\times \frac{1}{3}$

⇒ $\frac{1\times 1}{2\times 3}$

⇒ $\frac{1}{6}$  (Answer)