The blue taxis company operates 15 of the taxis in a certain...

The Blue Taxis company operates 15% of the taxis in a certain city, and Green Taxi operates the other 85%. After an accident at night in which a taxi was involved, a witness claimed that the vehicle was blue. Presumably, the inhabitants are used to seeing only blue or green taxis. Suppose that, under night vision conditions, 83% of individuals can correctly distinguish between blue and green. a) What is the probability that the witness saw a blue taxi? b) What is the probability that the taxi was actually blue if the witness says it was blue?

Transcript

00:01 Hello, in this question we are given the following conditions.

00:03 Okay, there are total of 15 % of taxi in the city are blue and the remaining 85 % are green.

00:11 So probability of being a taxi blue or green is 0 .15 and 0 .85 respectively.

00:18 Okay, and a person sees correctly by 83 % of chances.

00:24 So if he sees a blue taxi and he will report it correct, then it would be blue with a percentage of 83 and it will report it incorrect and it would be green with a percentage of 0 .817.

00:35 Similarly in case of green if he sees it is correct it would be 0 .83 % chance that he will report it as a green or 0 .17 probability that it will report it as a blue.

00:51 Okay so being a blue taxian reported blue it has a probability of 0 .1.

01:03 8 3 into 0 .15.

01:10 So let me calculate this value.

01:14 0 .83 into 0 .15.

01:17 So it is coming out to be 0 .125.

01:21 So given that it was really blue taxi but reported green has a probability of 0 .15 into 0 .17.

01:33 So this value would come out to be 0 .05 .025 .025.

01:34 So this value would come out to be 0 .055.

01:40 Okay, so and given it was a green taxi and reported correctly, then the probability of being a green was 0 .85 into 0 .83.

01:51 It is 0 .75.

01:58 And being a green taxi and reported blue, it has a probability 0 .85 into 0 .17.

02:07 So this value would be 0 .1445.

02:17 Okay, so now let us answer the questions.

02:20 In the first question, it says that what is, if the witness claimed that the taxi was blue, okay? it was, it is given that he claimed the taxi was blue.

02:31 So these two cases are our sample, sample spaces.

02:36 So for the a part, what do we need to answer? we need to answer that what is the probability that the witness says saw a blue taxi it means that we need to answer that it was really a blue taxi if the witness says it was a blue so the total sample space is 0 .1445 plus 0 .1245 and our favorable cases is that he saws a blue and reported a blue so it is 0 .125 so this would be the answer let me correct calculated 0 .1245 plus 0 .1445...

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