In a village 3/5 of the pensioners have had a flu injection.
If a pensioner has had the flu injection the probability of catching flu is 1/30.
If a pensioner has not had the flu injection the probability of catching flu is 7/10.
(i) Calculate the probability that a pensioner, picked at random, from this village, catches the flu.
(ii) A statistician calculated that 120 pensioners from this village are expected to catch flu. Calculate how many pensioners live in this village.
Please show the working to your answer, and the procedure required to determine what method is needed.
If a pensioner has had the flu injection the probability of catching flu is 1/30.
If a pensioner has not had the flu injection the probability of catching flu is 7/10.
(i) Calculate the probability that a pensioner, picked at random, from this village, catches the flu.
(ii) A statistician calculated that 120 pensioners from this village are expected to catch flu. Calculate how many pensioners live in this village.
Please show the working to your answer, and the procedure required to determine what method is needed.
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(i) P(had injection and gets flu) = 3/5 x 1/30 = 1/50
P(not had injection and gets flu) = 2/5 x 7/10 = 14/50
P(gets flu) = 1/50 + 14/50 = 15/50 = 3/10
(ii) Expected number of pensioners getting flu = 3/10 x number of pensioners = 120
number of pensioners = 120 ÷ 3/10 = 120 x 10/3 = 1200/3 = 400
P(not had injection and gets flu) = 2/5 x 7/10 = 14/50
P(gets flu) = 1/50 + 14/50 = 15/50 = 3/10
(ii) Expected number of pensioners getting flu = 3/10 x number of pensioners = 120
number of pensioners = 120 ÷ 3/10 = 120 x 10/3 = 1200/3 = 400