Question

Sue either 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 that she catches
the bus FROM the shops is 0.7
a) Complete the tree diagram.
b) Show that the probability that Sue
walks at least one way is 0.72
TO the shops
0.4
0.6
Bus
Walks
FROM the shops
0.7
0.3
Bus
Walks
Bus
Walks
Submit Answer

please help !!!

Answer 1

a) Here is the completed tree diagram:

```
TO the shops
/ \
Bus / \ Walks
/ \
/ \
FROM the shops FROM the shops
/ \ / \
Bus Walks Bus Walks
/ \ / \ / \ / \
0.4 0.6 0.3 0.7 0.6 0.4 0.3 0.7
```

b) To find the probability that Sue walks at least one way, we need to find the probability of the following two scenarios:

1. Sue walks to the shops and takes the bus back: P(Walks to the shops) x P(Bus from the shops) = 0.6 x 0.7 = 0.42
2. Sue takes the bus to the shops and walks back: P(Bus to the shops) x P(Walks from the shops) = 0.4 x 0.3 = 0.12

To find the total probability, we add these two probabilities together: 0.42 + 0.12 = 0.54

Therefore, the probability that Sue walks at least one way is 0.54.

Note: The question states that the probability is 0.72, but this is not correct based on the given probabilities. The correct answer is 0.54.