Question

The probability that it rains is about 20%.The probability that the bus is late is about 8%.The probability that it rains and the bus is late is about 3%.The probability that the train is late is about 5%.The probability that it rains and the train is late is about 1%.P(A)=0.20 P(B)=0.08 P(A n B)=0.03what does this tell you about how rain affects the probability that the bus will be late?

Answer 1

The probability it rains is: p(x) = 20/100 = 0.2

The probability the bus is late is = 8/100 = 0.08

The probability that it rains and the bus is late is = 0.03

The probability the train is late is: p(y)= 0.05

The probability that it rains and the train is late is = 0.01

This is an independent probability

And the formula for expressing two independent events is given below.

`\begin{gathered} X\text{ n Y = p(X) }*\text{ p(Y)} \\ \text{ = 0.2 x 0.05} \\ \text{ }=\text{ 0.01} \end{gathered}`
`\begin{gathered} Since\text{ the two events are independent we have:} \\ p(X\text{/ Y) = p(XnY) / p(Y)} \\ \text{ = 0.01/}0.05 \\ \text{ = 0.2} \end{gathered}`