Question

# 1. Suppose that A, B are two independent events, with P(A) = 0.3 and P(B) =...

1. Suppose that A, B are two independent events, with P(A) = 0.3 and P(B) = 0.4.
Find P(A and B)

a. 0.12

b. 0.3

c. 0.4

d. 0.70

2. Experiment: choosing a single ball from a bag which has equal number of red, green, blue, and white ball and then rolling a fair 6-sided die.

a.) List the sample space.

b.) What is the probability of drawing a green ball and even number?

2.

solution:

It is given that the A and B are independent event, and P(A) = 0.3, and P(B) = 0.4

so, P(A and B) = P(A) * P(B)

PA and B) = 0.3*0.4 = = 0.12

so corrrect answer is a) 0.12

2)

let R, G and B be the event of drawaing red, green and blue ball from the bag

it is given that the number of red, green and blue balls are equal in the bag.

so, P(R) = P(G) = P(B) = 1/3

sample space of drawing a ball and then rolling a die. as follows

a)

(R,1), (R,2) (R,3), (R,4),(R,5) , (R,6)

(G,1), (G,2) (G,3), (G,4),(G,5) , (G,6)

(B,1), (B,2) (B,3), (B,4),(B,5) , (B,6)

b)

total possible outcomes = 18

P(G and Even)

number of favaorable cases for the given event are = (G,2), (G,4), (G,6) = 3

P(G and Even) = 3/18 = 0.1667