3.13 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: 3.13 (page 188)

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). Let T be the event of getting the white ball twice, F the event of picking the white ball first, S the event of picking the white ball in the second drawing.
a. Compute P(T).
b. Compute P(T|F).
c. Are T and F independent?.
d. Are F and S mutually exclusive?
e. Are F and S independent?

Short Answer

Expert verified

P(T) = $1 / 4$ ; P (T | F) = $1 / 4$

T & F are not independent ; F & S are not mutually exclusive ; F & S are independent.

Step by step solution

Probabilities calculation

$P r (T)$ = P (getting white ball twice)

Pr (getting white ball once) = $1 / 2$ ; P (get white ball again, with replacement) = $1 / 2$

So, $P (T)$ = $1 / 2 x 1 / 2 = 1 / 4$

$P r (T I F)$ = Pr getting white ball twice, given first ball is white

= $P (T 鈭� F) / P (F)$

= ( 1 /4 ) / ( 1 / 2 )

= 1 / 2

Independent & mutually exclusive events

Independent Events are those where occurrence of one event doesn't effect the occurrence of other event. Mutually Exclusive events are those which cannot happen simultaneously.

Events T & F are not independent, as event F ie getting first white ball effects event T ie getting the white ball twice.
Events F & S are not mutually exclusive, as event F ie getting first white ball & event S picking the second white ball - can happen together
Events F & S are independent, as event F ie getting first white ball & event S picking the second white ball - do not effect each other.