Question

A group of ducks being raised on a farm are categorized according to gender and breed. The results are in the table below.

	Pekin	Crested	Runner	Total
Male	42	4	18
Female	57	5	7
Total

1. Complete the table above

If one of these ducks is to be selected at random, find the probability that the duck is

1. 2. Female (give 2 decimal places)
2. 3. A Runner duck (give 2 decimal places)
3. 4. Not a Pekin duck (give 2 decimal p!aces)

e}    Male or a Crested duck (give 2 decimal places)

f)    Would it be unusual for a randomly selected duck to be a female runner duck? Explain.

Answer 1

a.

The completed table with total are as follows.

	Pekin	Crested	Runner	Total
Male	42	4	18	64
Female	57	5	7	69
Total	99	9	25	133

b.

If one of these ducks is to be selected at random, the probability that the duck is female

= Number of female ducks / Total number of ducks

= 69 / 133

= 0.52

If one of these ducks is to be selected at random, the probability that the duck is female is 0.52.

c.

If one of these ducks is to be selected at random, the probability that the duck is runner

= Number of runner ducks / Total number of ducks

= 25 / 133

= 0.19

If one of these ducks is to be selected at random, the probability that the duck is runner is 0.19.

d.

If one of these ducks is to be selected at random, the probability that the duck is not a Pekin duck

= Number of non Pekin ducks / Total number of ducks

= (9 + 25) / 133

= 34 / 133

= 0.26

If one of these ducks is to be selected at random, the probability that the duck is not a Pekin duck is 0.26.

e.

If one of these ducks is to be selected at random, the probability that the duck is a male or a Crested duck

= (Number of male ducks + Number of Crested ducks - Number of male crested ducks) / Total number of ducks

= (64 + 9 - 4) / 133

= 69 / 133

= 0.52

If one of these ducks is to be selected at random, the probability that the duck is a male or a Crested duck is 0.52.

f.

If one of these ducks is to be selected at random, the probability that the duck is a female runner duck

= Number of female runner duck / total number of ducks

= 7 / 133

= 0.05

If one of these ducks is to be selected at random, the probability that the duck is a female runner duck is 0.05.

It is unusual for a randomly selected duck to be a female runner duck as the probability is only 5%.