Respuesta :
Answer:
Probability of exactly 3 red balls = 0.2652
Step-by-step explanation:
We are given that an urn has 5 red balls and 7 blue balls.
And we randomly select 5 balls from the urn and have to find the probability that your hand has exactly 3 red balls.
Firstly, number of ways of selecting 3 red balls from total of 5 red balls in the urn = [tex]^{5} C_3[/tex] = [tex]\frac{5!}{3!*2!}[/tex] = 10
Now since 5 balls have to be selected so remaining 2 balls will be blue only, so number of ways of selecting 2 blue balls from total of 7 blue balls in the urn = [tex]^{7} C_2[/tex] = [tex]\frac{7!}{2!*5!}[/tex] = 21
The total number of ways of selecting 5 balls from total of 12 balls in the urn = [tex]^{12} C_5[/tex] = [tex]\frac{12!}{5!*7!}[/tex] = 792
So, probability that your hand has exactly 3 red balls = [tex]\frac{^{5} C_3* ^{7} C_2}{^{12} C_5}[/tex]
= [tex]\frac{10*21}{792}[/tex] = 0.2652 .
