- #1
silkdigital
- 4
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Question:
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!
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!