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Dreamboat cars are produced at three different factories A, B, and C. Factory A produces 20% of the total output of Dreamboats, B 50%, and C 30%. However, 5% of the cars at A are lemons, 2% at B are lemons, 10% at C are lemons. If you buy a Dreamboat and it turns out to be a lemon, what is the probability that it was produced at factory A?

My workings were:

0.05 / (0.05 + 0.02 + 0.1) = 29.41%

I ignored the output percentages because the base condition is that the car is a lemon already. Is my logic on the right track? Not sure if I'm correct!

Another tough question is this:

Suppose that 10 cards, of which 7 are red and 3 are green, are put at random into 10 envelopes, of which seven are red and three are green, so that each envelope contains one card. Determine the probability that exactly k envelopes will contain a card with a matching color.

I've managed to obtain k=4

[7C4 * 3C3] / 10C7

and k=10

[7C7 * 3C0] / 10C7

Not sure what the next steps are to express in terms of any k. Hope that makes sense.

Thanks for any help in advance, having some difficulty!

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# Stuck on a probability question

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