Answer to Question #306842 in Statistics and Probability for Armani

Question

A class consists 8 boys and 16 girls of which half the boys and haf the girls have blood group B. A student is selected at random what is the probability that the student is a boy or has B blood group

Answer 1

• Let P(B) be the probability that the chosen student is a boy
• Let P(GB) be the probability that the chosen student has blood group B
• Let P(B&GB) be the probability that the chosen student is a boy and has blood group B
• Let P(B/GB) be the probability that the chosen student is a boy or has blood group

$P(B)=\dfrac{8}{24}=\dfrac{1}{3}$

$P(GB)=\dfrac{1}{2}$

$P(B and GB)=\dfrac{8}{24} × \dfrac{1}{2}=\dfrac{1}{6}$

$P(B or GB)=P(B)+P(GB)-P(B and GB)$

$=\dfrac{1}{3}+\dfrac{1}{2}-\dfrac{1}{6}=\dfrac{2}{3}$