Answer to Question #155262 in Statistics and Probability for Cameron

Question

Michael likes to go for daily jogs with his dog, Max. If the weather is nice, he is 90% likely to jog for 5km. If the weather is rainy, he is only 55% likely to jog for 5km. The weather forecast for tomorrow indicates 40% chance of rain. Determine the probability that Michael will jog for 5km.

Answer 1

Let $E_1,E_2$ and $A$ are three events defined as follows:

$E_1=$ Weather forecast is nice

$E_2=$ Weather forecast is rainy

$A=$ Michael will jog for $5$ km.

Then $P(E_1)=\frac{60}{100}$

$P(E_2)=\frac{40}{100}$

and $P({A}/{E_1})= \frac{90}{100}$

$P({A}/{E_2})= \frac{55}{100}$

Then the required probability that Michael will jog for $5$ km is

$P(A)=P(E_1).P({A}/{E_1})+P(E_2).P({A}/{E_2})$

$=\frac{60}{100}.\frac{90}{100}+\frac{40}{100}.\frac{55}{100}$

$=\frac{54}{100}+\frac{22}{100}$

$=\frac{76}{100}$

$=0.76$