Forrest has determined that if he gets to the bus stop at 7:30 am, there is a 0.15 probability that he misses the bus. If

he arrives at the bus stop three consecutive days at 7:30, what is the approximate probability that he catches the bus all

three days?

Answer: 0.614

Step-by-step explanation:

First find the probability that he catches the bus in a day.

Probability of catching bus once = 1 - Probability of missing bus

= 1 - 0.15

= 0.85

If he arrives on 3 consecutive days at 7:30 am, the probability he will catch the bus is:

= (P | Day 1) * (P | Day 2) * (P | Day 3)

= 0.85 * 0.85 * 0.85

= 0.614

The approximate probability that he catches the bus all  three days is 0.614.

Given that,

Forrest has determined that if he gets to the bus stop at 7:30 am, there is a 0.15 probability that he misses the bus.

If  he arrives at the bus stop three consecutive days at 7:30,

We have to determine,

What is the approximate probability that he catches the bus all  three days.

According to the question,

The probability that he catches the bus in a day.

Probability of catching bus once = 1 - Probability of missing bus,

= 1 - 0.15

= 0.85

If he arrives on 3 consecutive days at 7:30 am,

Then, the probability he will catch the bus is:

= (P | Day 1) × (P | Day 2) × (P | Day 3)

= 0.85 × 0.85 × 0.85

= 0.614

Hence, The approximate probability that he catches the bus all  three days is 0.614.

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