CT10
What is P(# of H out of 4 tosses >= # of H out of 5 tosses)?
CT10 - Answer:
1/2 (symmetry consideration)
CT11
Flip n unbiased coins. What is P(# of H = n/2)?
CT11 - Answer:
nC_(n/2)/2^n
CT12
Toss 4 coins and win the number of H. There is an option to re-toss. What is the value of the game?
CT12 - Answer:
([1 4 6 4 1] * [2 2 2 3 4]') / 16 = $2.375 (dynamic programming/backward induction)
CT13
What is the expected product of (# of H) * (# of T) when tossing 10 fair coins? (Hint: the answer is not 25)
CT13 - Answer:
22.5 (E[(# of H) * (10 - # of H)])
CT14
Keep flipping a fair coin. What is the probability that the sequence HHT appears before THH does?
CT14 - Answer:
1/4 (Once you have T, THH would always precede HHT; likewise, once you have HH, HHT would always precede THH)
CT15
Toss 4 coins and win the number of H. There is an option to re-toss one coin. What is the value of the game?
CT15 - Answer:
2 + 0.5 * 15/16 = $2.469 (dynamic programming/backward induction)
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