Question

During our morning commute we encounter two traffic lights which are distant from one another and may be assumed to operate independently. There is a 50% chance that we will have to stop at the first of the lights, and there is a 30% chance that we’ll be stopped by the second light. Find the probability that we are stopped by at least one of the lights

Answer 1

Answer:-

Given that:-

During our morning commute we encounter two traffic lights which are distant from one another and may be assumed to operate independently. There is a 50% chance that we will have to stop at the first of the lights, and there is a 30% chance that we’ll be stopped by the second light.

Find the probability that we are stopped by at least one of the lights?

The two traffic lights operate independently and there is a 50% chance that will have a stop at the first of the lights ,and There is a 30% chance that we will be stopped by the second light .

P(Stopped by first light) = 0.50

P(Stopped by second light) = 0.30

P(Stopped by both lights) = [Since thay operate independently]

  

Here,

we need to find the probability that we will be stopped by at least one of the lights .

P(Stopped bt at least one of the light) = P(Stopped by first light)+P(stopped by second light)-P(stopped by both light)

= 0.50+0.30-0.15

=0.95

Alternate method

P(stopped by at least one of the lights)= 1-P(stopped by n one of the lights)

= 1- P(not stopped by first light)*(not stopped by second light)

= 1- [(1-0.50)(1-0.30)]

= 1-[(0.50)(0.70)]

=1-0.35

=0.65