QUESTION 18 Albert is a farmer. He has three different breeds of cow. He has 280
ID: 2947922 • Letter: Q
Question
QUESTION 18 Albert is a farmer. He has three different breeds of cow. He has 280 cows altogether. One-quarter of his cows are Angus breed, 125 are Hereford and the rest are Ayrshire. Albert needs to test all his cows for a disease but has so far only been able to test 40% of each breed. (a) Complete the table to show this information. Angus Herefore Ayrshire Total Tested 28 50 34 112 Not Tested 42 75 51 168 Total 70 125 85 280 One of the cows is selected at random. (b) Work out the probability that the cow chosen is ‘Hereford’ and ‘not tested’. Round answer to four decimal places. Answer = 0.6000 (c) Work out the probability that the cow chosen is not an ‘Ayrshire’. Round answer to four decimal places. Answer = 0.6964 (d) Work out the probability that the cow chosen is either an ‘Angus’ or ‘tested’. Round answer to four decimal places. Answer = 1.000 (e) Work out the probability that among Herefore, a randomly chosen cow is ‘tested’. Round answer to four decimal places. Answer = 0.4000
Explanation / Answer
a)
b)
probability that the cow chosen is ‘Hereford’ and ‘not tested’=75/280=0.2679
c)
probability that the cow chosen is not an ‘Ayrshire’=1-P(Ayrshire)=1-85/280=0.6964
d)
probability that the cow chosen is either an ‘Angus’ or ‘tested’.=(70+112-28)/280=0.5500
e)
probability that among Herefore, a randomly chosen cow is ‘tested’=50/125=0.4000
angus hereford Ayrshire total tested 28 50 34 112 not tested 42 75 51 168 total 70 125 85 280