Answer to Question #278662 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)

$$10+15+8=33$$

i)

$$P(1W\&1B\&1G)=\dfrac{\dbinom{10}{1}\dbinom{15}{1}\dbinom{8}{1}}{\dbinom{33}{3}}=\dfrac{10(15)(8)}{5456}$$

$$=\dfrac{75}{341}\approx0.22$$

ii)

$$P(3W)=\dfrac{\dbinom{10}{3}\dbinom{15}{0}\dbinom{8}{0}}{\dbinom{33}{3}}=\dfrac{120(1)(1)}{5456}$$

$$=\dfrac{15}{682}\approx0.022$$

Or

$$P(3W)=\dfrac{10}{33}(\dfrac{9}{32})(\dfrac{8}{31})=\dfrac{15}{682}\approx 0.022$$

b)

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

Given $P(A)=p, P(B)=2p, P(A\cup B)=P.$

Then

$$P(A\cap B)=p+2p-P$$

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