Question

**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.

Answer #1

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**

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