A box contains red and blue marbles

MATHEMATICS · Multi-part · CBSE · Mathematics · Probability · Probability

Problem

A box contains

5

red and

3

blue marbles. Two marbles are drawn successively. (i) Without replacement between draws, compute

P(R_1)

P(R_2)

and

P(R_1\cap R_2)

, where

R_1

is the event “the first marble is red” and

R_2

is the event “the second marble is red.” (ii) On the basis of the results in part (i), state whether

R_1

and

R_2

are independent. Show complete reasoning. (iii) Now suppose the first marble is replaced before drawing the second one. Re-calculate

P(R_1)

P(R_2)

and

P(R_1\cap R_2)

and comment on the independence of

R_1

and

R_2

in this modified experiment.