Question

i am lost. there are multiple choices. i chose 54% and it was wrong. it has suggestions at tge bottom. it says to use tree diagram.

Answer 1

From the given information, we know that

`P(\text{bus and 7pm)=P(bus)}\cdot P(7pm)=0.83*0.62=0.5146`

because they are independent events. Similarly, we have

`P(car\text{ and 7pm)=P(car)}\cdot P(7pm)=(1-0.83)*0.14=0.0238`

Now, we need the conditional probability P(bus | 7pm), which can be given as

`P(\text{bus}|7pm)=\frac{p(\text{bus and 7pm)}}{\text{p(7pm)}}=\frac{p(\text{bus and 7pm)}}{p(\text{bus and 7pm)}+p(car\text{ and 7pm)}}`

By substituting our result into this last expression, we get

`P(\text{bus}|7pm)=(0.5146)/(0.5146+0.238)=(0.5146)/(0.5384)=0.9557`

By rounding up our result, the answer is 0.96, which corresponds to 96 %