Question

A magician's hat contains three types of rabbits: floppy-eared, white and baby rabbits.

a) Draw a Venn diagram to illustrate the contents of the magician's hat given that there are: 27 floppy-eared, 25 white, 34 baby, 15 floppy-eared and white, 9 floppy-eared baby, 5 white baby, and 3 floppy-eared white baby rabbits.

Suppose the magician selects one rabbit from the hat at random. Determine the probability that the magician chooses:

b) A baby rabbit.

c) A rabbit that is not white.

d) A floppy eared rabbit that is not a baby

Draw a histogram to represent the probability distribution for all the sums of TWO five-sided dice. (Hint: the sides of the dice are 1,2,3,4 & 5)

Answer 1

a)

let  floppy-eared, white and baby rabbits be represented by F,W,and B resp.

b)

total rabbit=n(F)+n(W)+n(B)-n(F n W)-n(F n B)-n(B n W)+n(F n W n B) =27+25+34-15-9-5+3= 60

P(a baby rabbit) = 34/60=0.56667

c)

P( A rabbit that is not white) = 1-P(white rabbit) = 1-25/60=0.5833

d)

P( A floppy eared rabbit that is not a baby) = 18/60=0.3

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