Question

Sue either travels by bus or walks when she visits the shops. The probability that she catches the bus from the shops is 0.7. Show that the probability that she walks at least one way is 0.72

Answer 1

Corrected Question

Sue travels by bus or walks when she visits the shops. The probability that she catches the bus to the shops is 0.4. The probability she catches the bus from the shops is 0.7. Show the probability that Sue walks at one way is 0.72

Answer:

`P(A \cup B) =0.72` (Proved)

Explanation:

Sue travels by bus or walks when she visits the shops.

Let the event that she catches the bus to the shop=A

Let the event that she catches the bus from the shop=B

P(A)=0.4

P(B)=0.7

Both A and B are independent events.

Therefore,Probability that she catches the bus to and from the shop:

P(A∩B) = 0.4 X 0.7= 0.28

Probability Sue walks at least one way
`P(A \cup B) = 1 - P(A \cap B)`

`= 1 - 0.28\\= 0.72`

Hence, the probability that Sue walks at least one way is 0.72.