Geometric An employer ranks three people equally, but can only hire one. The thr

Question

Geometric An employer ranks three people equally, but can only hire one. The three potential employees decide that they will resort to flipping coins. The game goes as follows: all three employees flip a coin with probability of heads=p, probability of tails=q. If one person has heads and the other two have tails, that person wins. Similarly, if one person has tails and the other two have heads, that person wins. What is the probability that someone will win in fewer than n tosses? Assume p = 1/2. What is the minimum number of tosses to ensure, with.95 probability, that someone wins?

Explanation / Answer

The game wins with following combination

pqq or qpp

in any order

a)If always first person flips the coin,

In first three tosses, if a person has to win,

pqq or qpp = (1/2)^3=1/8

In first six toxes

first 3 tosses ppp or qqq than next pqq or qpp = (1/2)^6

similarly for n tosses, = (1/2)^(n/3) where n is multiple of 3

other wise win or lose cannot be decided,

b) minimum games required = 3

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.