Problem 4.3.5. How important is a head start? You and I are participating in a q

Question

Problem 4.3.5. How important is a head start? You and I are participating in a quiz show. In the show, we take turns and at each turn each participant has to answer a question. The first to give a correct answer wins. We assume that the answers to the questions are independent of each other, and that for each player the probability of answering a question correctly is fixed. a. If each player answers each question correctly with probability p, what is the probability that the player to begin wins? b. Suppose we were told that the probability that the second player wins is 1/2. Find a relation between the probability that the first player answers a question correctly and the probability that the second player answers a question correctly

Explanation / Answer

(a) Pr(I Answer correctly) = Pr(You answer correctly) = p

Pr(Player A wins when he starts) = p + (1 -p)* (1-p) * p + (1-p)4 p + (1 -p)6 p = p [1/{1 - (1 -p)2}] = p [1/(2p - p2)] = 1/(2 -p)

so the probability that the player will win if he is the one to be begin with = 1/(2-p)

(b) Pr(First player answer as question correctly) = p + (1-p) * (1/2) * p + (1-p)2(1/2)2 * p + ...

= p [1 / {1 - (1-p)/2}]

= 2p/(1 + p)

so,

Pr(Second play wins) = 1 - 2p/(1 +p) = (1 + p - 2p)/(1 + p) = (1-p)/(2+p)

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

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