You are in a bar in Cape Town, South Africa and a disreputable character walks u
ID: 2930790 • Letter: Y
Question
You are in a bar in Cape Town, South Africa and a disreputable character walks up with a jar containing four large diamonds and six rough-cut rubies. He says that a real geologist should be able to distinguish the stones without looking into the jar, and he asks you to pick three gemstones out of the jar for a mere $ 100. If you pick two of one kind you get to keep the gems. Calculate the probability of picking two diamonds or two rubies in three attempts. Then calculate the odds of you surviving the night if you’re successful.
Explanation / Answer
The probability that the first pick is a diamond = 4/10
The probability that the second pick is also a diamond = 3/9
The probability that the third pick is a ruby given that the first two are diamonds = 6/8.
=> Probability that we pick two diamonds and one ruby in order = 4/10 * 3/9 * 6/8.
We can choose the order of the three gems in 3C2 = 3 ways.
=> Probability of choosing two diamonds and one ruby = 3 * 4/10 * 3/9 * 6/8.
The probability that the first pick is a ruby = 6/10
The probability that the second pick is also a ruby = 5/9
The probability that the third pick is a diamond given that the first two are ruby = 4/8.
=> Probability that we pick two rubies and one diamond in order = 6/10 * 5/9 * 4/8.
We can choose the order of the three gems in 3C2 = 3 ways.
=> Probability of choosing two rubies and one diamond = 3 * 6/10 * 5/9 * 4/8.
Therefore the probability of picking two of a kind = 3 * 4/10 * 3/9 * 6/8 + 3 * 6/10 * 5/9 * 4/8
= 0.8.
(Note: The last statement does not seem to mean anything. What does surviving the night mean?)
Odds of winning = 8 : 2.
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