Question

Consider a box containing 8 red, 10 blue and 12 yellow balls. Draw three balls one by one with replacement. Then answer the following questions:

a) Write down the sample space

b) Calculate the probability that there is at least one red ball

c) What is the probability that the first two balls are red

d) Calculate the probability that the first two balls are red given at least one ball is red?

e) What can you conclude based on c and d?

Answer 1

let R,B and Y are event of red,blue and yellow ball drawn

a)

sample space ={RRR,RRB,RRY,RBY,RYB,RBB,RYY,RBR,RYR,BBB,BBR,BRB,BBY,BYB,BRR,BYY,BRY,BYR,YYY,YYB,YYR,YRR,YBB,YRY,YBY,YRB,YBR}

b)probability that there is at least one red ball =19/27 (as there are 19 events in which there is at least one red)

c)

P(first two balls are red)=3/27 =1/9 (3 events in whihc first 2 balls are red)

d)

probability that the first two balls are red given at least one ball is red

=3/19 (as out of 19 events where at least one ball is red ; 3 have first 2 balls red)

e)

we conculude that  events first two balls are red and at least one ball is red are not independent ; as

probability that the first two balls are red given at least one ball is red is not equal to probability that the first two balls are red