Answer:the probability that a pensioner catches a flu is 0.3 or [tex]\frac{3}{10}[/tex]
Step-by-step explanation:
Data:
a) Pensioners who have had a flu jab = [tex]\frac{3}{5}[/tex]
b) Pensioners who did not had a flu jab = 1 - [tex]\frac{3}{5}[/tex] = [tex]\frac{2}{5}[/tex]
For the first pair of arrows: a is the probability of the upper arrow and b is the probability of the lower arrow.
If pensioner have had a flu jab, the probability of catching flu is [tex]\frac{1}{30}[/tex]
Data:
c) Catching flu = [tex]\frac{1}{30}[/tex]
d) Not catching flu = 1 - [tex]\frac{1}{30}[/tex] = [tex]\frac{29}{30}[/tex]
The second pair of arrows on the top: Top arrow is c and bottom arrow is d
If pensioner did not have a flu jab, the probability of catching flu is [tex]\frac{7}{10}[/tex]
Data:
e) Catching flu = [tex]\frac{7}{10}[/tex]
f) Not catching flu = 1 - [tex]\frac{7}{10}[/tex] = [tex]\frac{3}{10}[/tex]
The second pair of arrows on the bottom: Top arrow is e and bottom arrow is f.
Q) Probability pensioner catches a flu
P(catches the flu given that he had the flu jab) + P(catches the flu given that he did not have the flu jab)
([tex]\frac{3}{5}[/tex] x [tex]\frac{1}{30}[/tex]) + ([tex]\frac{2}{5}[/tex] x [tex]\frac{7}{10}[/tex] )
= 0.02 + 0.28
= 0.3
Therefore, the probability that a pensioner catches a flu is 0.3 or [tex]\frac{3}{10}[/tex]
Keyword: Probability
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