The probability that any single driver will turn left at an...

Name: The probability that any single driver will turn left at an intersection is .2. The left turn lane at this intersection has room for three vehicles. If the left turn lane is empty when the light turns red and five vehicles arrive at this intersection while the light is red, find the probability that the left turn lane will hold the vehicles of all of the drivers who want to turn left.
Uploaded: 2021-07-06T23:39:14-08:00
Duration: 7 min 44 s
Channel: Jacquelinne S. Mejia Sandoval
Description: The probability that any single driver will turn left at an intersection is .2. The left turn lane at this intersection has room for three vehicles. If the left turn lane is empty when the light turns red and five vehicles arrive at this intersection while the light is red, find the probability that the left turn lane will hold the vehicles of all of the drivers who want to turn left.

The probability that any single driver will turn left at an intersection is .2. The left turn lane at this intersection has room for three vehicles. If the left turn lane is empty when the light turns red and five vehicles arrive at this intersection while the light is red, find the probability that the left turn lane will hold the vehicles of all of the drivers who want to turn left.

Transcript

00:01 Hello everyone, this is problem 204.

00:05 Okay, so just imagine you're an observer in a cross -section.

00:16 And cars turn left, they turn right, or they keep going straight, correct? so imagine that there's a red light and there are no cars yet.

00:32 And then suddenly five cars appear, right? but on the left lane, only three cars could fit.

00:43 And we're trying to find the probability that those three cars, so five cars reach that intersection, but only three cars will be turning left.

00:58 So the other two cars will have to turn another direction.

01:05 That's what we're trying to figure out.

01:07 And they give us that the probability to turn left is 0 .2.

01:18 So think about it, right? if the problem to turn left is your point two, then we could just use the complement rule, right? to figure out the probability to not turn left.

01:29 So we could just do what? the complement rule, 1 minus 0 .2.

01:36 It will get 0 .8, right? so the probability of not turning left is 0 .8.

01:51 And we will use this later.

01:54 All right.

01:55 So we have two situations.

01:58 You're either going to turn left or you're not going to turn left.

02:03 So you could think, oh, wait, is it a bernoulli? well, it would be the sum of bernoulli's, wouldn't it be? because it's not just one event that we're talking about.

02:15 We're talking about three cars that have to turn left...

Question

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