Answer to Question #278663 in Statistics and Probability for Luckson

Question

a bag 10 white, 15 red and 8 green balls. A single draw of 3 balls is made. i)what is the probability that a white, a red and green balls are drawn

ii)What would be the probability of getting all the three white ball?

b) A and B are two events, not mutually exclusive, connected with a random experiment E, If P(A)=p, P(B)=2p and P(AuB)=P

Answer 1

a)

i)

$P=\frac{10\cdot15\cdot8}{C^{33}_3}=\frac{1200\cdot 3!30!}{33!}=0.2199$

ii)

$P=\frac{C^3_{10}}{C^{33}_3}=\frac{10!\cdot 3!30!}{33!3!7!}=0.0220$

b)

If the events A and B are not mutually exclusive, then:

$P (A \cup B) = P(A) + P(B) – P (A \cap B)$

so,

$P (A \cap B)= P(A) + P(B) -P (A \cup B) =3p-P$