(10 points each) Note: This is adapted from a Google interview question. I have

Question

(10 points each) Note: This is adapted from a Google interview question. I have a jar with 100 quarters. Most of them are regular (fair) quarters, but 7 of them are fake! These 7 fake quarters have heads on both sides a. If you select a coin from the jar at random and flip it 3 times and get heads every time, what is the probability that this is a regular quarter? b. Repeat the calculation in part a) but this time you flip the coin k times, getting heads each time. What is the probability that this is a regular quarter (in terms of k)?

Explanation / Answer

a) P( 3 heads on regular quarter) = 1/2^3 = 1/8

P( regular/3 heads) = 93/100* 1/8/[93/100*1/8 + 7/100 * 1]= 0.6241

b)P( regular/k heads0=93/100* 1/2^k/ [93/100*1/2^k + 7/100 * 1]

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