APPLICATIONS

Balls in a Jar Jar A contains three red balls and four white balls. Jar B contains five red balls and two white balls. Which one of the following ways of randomly selecting balls gives the greatest probability of drawing two red balls?

(i) Draw two balls from Jar B.

(ii) Draw one ball from each Jar.

(iii) Put all the balls in one Jar, and then draw two balls.

To find:

The greatest probability of drawing two red balls.

Given:

Jar A contains 3 red balls and 4 white balls. Jar B contains 5 red balls and 2 white balls.

Approach:

The probability of an event E of a sample space S is written as P(E) and is given by,

P(E)=n(E)n(S)=number of favorable outcomesnumber of total​ outcomes …(1)

The number of combinations of selecting r objects from a total of n objects is

C(n,r)=n!r!(n−r)! …(2)

Calculation:

For case (i),

Event E1=two balls from jar B.

n(E1)=C(5,2)=5!2!(5−2)!=5×4×3!2!3!=10

n(S)=C(7,2)=7!2!(7−2)!=7×6×5!2!5!=21

P(E1)=1021=0.4761

For case (ii),

Event E2=one ball from each​ jar