100 Tom has a coin with probability p2 of a head and Dick has a coin with probab
ID: 3126437 • Letter: 1
Question
100 Tom has a coin with probability p2 of a head and Dick has a coin with probability pi of a head. Tom and Dick alternate tossing their coins, with Tom going first. The first person Find the probability that Tom wins. Evaluate the probility in part (a) if both coins are balanced. What must be the relationship between p and pi to make the game fair? If Dick's coin is balanced, what must be the probability of a head for Tom's coin to make the game fair? Evaluate the probability in part (a) if both coins are balanced.Explanation / Answer
answer a)
probability of wininng tom is like this=H, TTH, TTTTH, TTTTTTH......=first,third,fifth.....
p1,(1-p1)(1-p2)p1,(1-p1)(1-p2)(1-p1)(1-p2)p1,........=p1(n=1),(1-p1)(1-p2)p1(n=3),((1-p1)(1-p2))2p1(n=5),...,,((1-p1)(1-p2))np1(n=2n+1)
required probability=((1-p1)(1-p2))np1(n=2n+1)
as in first tossing Tom get head and win is p1, otherwise Dick will toss the coin and he would not win if he get tail with probability 1-p2 and so on
answer b)
if both coin are balanced then p1=p2=1/2
so requied probability=(1/2)2n+1
answer c)game would be fair if p1=p2
answer d)if dick coin is balanced it means p2=1/2 so p1 should be 1/2 to make the fame fair
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.