Respuesta :
Answer:
The probability that Sonia picks a yellow hair clip and a blue hair clip without replacement = [tex]\frac{1}{6}[/tex]
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 = [tex]5+2+3[/tex] = 10
The probability that Sonia picks a yellow clip from the lot will be :
⇒ [tex]\frac{\textrm{Number of yellow clips}}{\textrm{Total number of clips}}[/tex]
⇒ [tex]\frac{5}{10}[/tex]
Simplifying fraction by dividing both numbers by their G.C.F.
⇒ [tex]\frac{5\div 5}{10\div 5}[/tex]
⇒ [tex]\frac{1}{2}[/tex]
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 = [tex]10-1[/tex] = 9
The probability that Sonia picks a blue clip from the remaining lot will be :
⇒ [tex]\frac{\textrm{Number of blue clips}}{\textrm{Total number of clips}}[/tex]
⇒ [tex]\frac{3}{9}[/tex]
Simplifying fraction by dividing both numbers by their G.C.F.
⇒ [tex]\frac{3\div 3}{9\div 3}[/tex]
⇒ [tex]\frac{1}{3}[/tex]
The probability that she picks a yellow hair clip and a blue hair clip without replacement can be given as:
⇒ [tex]\frac{1}{2}\times \frac{1}{3}[/tex]
⇒ [tex]\frac{1\times 1}{2\times 3}[/tex]
⇒ [tex]\frac{1}{6}[/tex] (Answer)
