Q3.7 A box has two balls, one white a... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 3: Q3.7 (page 184)

A box has two balls, one white and one red. We select one ball, put it back in the box, and select a second ball (sampling with replacement). Find the probability of the following events:
a. Let F = the event of getting the white ball twice.
b. Let G = the event of getting two balls of different colors.
c. Let H = the event of getting white on the first pick.
d. Are F and G mutually exclusive?
e. Are G and H mutually exclusive?

Short Answer

Expert verified

Probabilities : a) = $1 / 4$ ; b) $1 / 2$ ; c) $1 / 2$

d) Event F and G are mutually exclusive. e) Event G and H are not mutually exclusive.

Step by step solution

Probability - Concept and Solution

Probability is the likelihood of an event, calculated by favourable outcomes / total outcomes

Probability of getting a white ball = White Ball / Total Balls = $1 / 2$
Probability of getting a red ball = Red ball / Total balls = $1 / 2$

a) Probability of getting white ball twice = $1 / 2 x 1 / 2 = 1 / 4$

b) Probability of getting 2 balls of different colours = Pr [ (White & red ball) or( red & white ball) ] = $(1 / 2 x 1 / 2) + (1 / 2 x 1 / 2) = 1 / 4 + 1 / 4 = 2 / 4 = 1 / 2$

c) Probability of getting white ball on the first pic = Pr (White ball on first pick & any ball on second pick) = $(1 / 2) 鈥� x (2 / 2) = (1 / 2) x 1 = 1 / 2$

Mutually Exclusive - Concept and Solution

Mutually Exclusive Events are those, which can't happen at the same time.

Examples : If a coin is tossed, both a head and tail can't come.

A car can't move backward & forward at the same time.

d) Events F & G are mutually exclusive as - there are total two balls (one white & one red), and event of getting white ball twice & two balls of same colour can't happen together.

e) Events G & H are not mutually exclusive - as out of two balls (one white & one red), it is possible that we get white on the first pick and get two balls of different colours. It can happen when first ball is white & second red.