Maths and Stats , 2015 paper

The ratio of male to female calves being kept in the herd after three months is about one male to every seven females. This is to be changed to one male to every ten females.

If the number of male calves remain the same, what proportion of females would have been sold?

Thank you.

This question follows and requires information from the previous questions.

Answering question 3a(iii) you found that percentage of male calves retained after three months:

P (male retained)=0.55 * 0.3 * 0.2=0.033

0.55 males caves were born, 0.3 retained after the first months and out of these 0.2 retained after the third months. (Say, out of thousand calves born you would have retained 33 males)

We know that male to female ratio is to be changed to 1:10 thus we should have 10 times more female than male calves retained:

P(females retained) = 0.033 * 10 = 0.33
(Out of thousand calves born you would have 33 male and 330 female calves retained)

We know that originally we had 0.45 female calves (out of thousand calves born 450 were female), therefore

P(females sold) = 0.45 - 0.33 = 0.12

(out thousand calves that would be 450 - 330 = 120)

We were asked to find proportion of female calves being sold. We know that 0.12 calves out of 0.45 were sold, thus:

0.12/0.45 = 0.267 or 26.7%

(or 120 female calves out 450 that were born)

I hope that helps. Please ask if you need more clarification.

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