Question

When you order a Lyft, the probability that you get a Subaru is 0.4. Further, the probability that you get a white car is 0.3, and that you will get a white Subaru is 0.2. Find the probability that,

1. You will get a non-white, non-Subaru car
2. You will get a white, non-Subaru car

Answer 1

Let the probability of Subaru be P(S) therefore non subaru P(S')

and white car be denoted by P(W) therefore non white P(W')

P(S) = 0.4 P(S') = 1 - 0.4 = 0.6

P(W) = 0.3 P(W') = 0.7

White and Subaru means the intersection therefore = 0.2

Using the additional rule we have

= 0.4 + 0.3 - 0.2

= 0.5

You will get a non-white, non-Subaru car

It is denoted by

We have the identity

= 1 - 0.5

here the L.H.S. represents none where as the R.H.S. 2nd part denotes at least one. Since these two are complements we use the identity.

You will get a white, non-Subaru car

With a white car we can either have a subaruor a non-subaru

Therefore

= 1 - 0.2