Finding probability that events WONT occur?

[kay43]

I'm struggling to understand which formula/way to go about this question: There are 7 cars, 2/7 have a leak and 4/7 don't have coolant. Whats the probability that the first car he services has neither problem?

I understand how I would find the probability that a car has an issue, but struggling to incorporate the probability that its the first car he picks. Can anyone break this down into easier terms for me?

 

[Romsek]

You really can't answer this question with the information given.

Suppose 2 cars have both a leak and don't have coolant, and then 2 more are just lacking coolant.
Then there are 3 cars that have no problems at all.

On the other hand suppose that 2 cars have a leak, and 4 different cars have lack coolant.
Then there is only 1 car that has no problems.

You need to know how many cars have both problems.

 

[kay43]

You really can't answer this question with the information given.

Suppose 2 cars have both a leak and don't have coolant, and then 2 more are just lacking coolant.
Then there are 3 cars that have no problems at all.

On the other hand suppose that 2 cars have a leak, and 4 different cars have lack coolant.
Then there is only 1 car that has no problems.

You need to know how many cars have both problems.

In order to find how many cars with both problems, would I just compute 2/7 * 4/7 = .16 cars have both problems, .28 have leak and .57 have coolant issues. Wouldn't that just mean that all cars have problems?

 

[Deleted member 4993]

In order to find how many cars with both problems, would I just compute 2/7 * 4/7 = .16 cars have both problems, .28 have leak and .57 have coolant issues. Wouldn't that just mean that all cars have problems?

If you can assume that those two events [having a leak (where?) and having no coolant (how did the coolant get lost?)] are independent then the chance of having neither is [1 - (2/7 + 4/7 - 8/49) = 1 - 34/49 = ]15/49. That is more than 2/7.

However, these computations make sense when the population is large.