Ekene and Amina

The probability that Ekene will be alive in 5 years' time is 3/4, and the probability that his wife Amina will be alive in 5 years' time is 2/5. Find the probability that in 5 years' time:
a) both of them will be alive
b) only Ekene will be alive

Correct answer:

a =  0.3
b =  0.45

Step-by-step explanation:

$$\begin{gathered} p_1=\frac{3}{4}=0.75 \\ {p}_2=\frac{2}{5}=0.4 \\ a=p_1\cdot p_2=\frac{3}{4}\cdot \frac{2}{5}=\frac{3\cdot 2}{4\cdot 5}=\frac{6}{20}=\frac{3}{10}=0.3 \end{gathered}$$

$$\begin{gathered} p_3=1-p_2=1-\frac{2}{5}=\frac{1\cdot 5}{5}-\frac{2}{5}=\frac{5}{5}-\frac{2}{5}=\frac{5-2}{5}=\frac{3}{5}=0.6 \\ b=p_1\cdot p_3=\frac{3}{4}\cdot \frac{3}{5}=\frac{3\cdot 3}{4\cdot 5}=\frac{9}{20}=0.45 \end{gathered}$$

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