Two players share an unbiased coin and take it in turns to play "the race". On player 1's turn, he tosses the coin once: if it comes up heads, he scores one point; if it comes up tails, he scores nothing. On player 2's turn, she chooses a positive integer and tosses the coin times: if it comes up all heads, she scores points; otherwise, she scores nothing. Player 1 goes first. The winner is the first to or more points.
Answers
Answer:
for t = 2 she has maximum probability to win
Step-by-step explanation:
Player 1 getting head probability = 1/2
to Score 100 points he probably needs 200 turns
Player 2 select number t
Probability that all head turned up = (1/2)^t
Points she get = 2t-1
let say t = 1
probability of turning head = 1/2
Point she get = 2*1 - 1 = 1
to score 100 point probably she need 200 turns
she turns second so she has lesser chance to win
let say t = 2
probability of turning head = (1/2)² = 1/4
Probability she won in a turn is 1 out of 4
Point she get = 2*2 - 1 = 3
to score 100 or more point probably she need to win min 34 turns so turns required to win 34 time = 34 * 4 = 136 turns only
She has more chances to win
let say t = 3
probability of turning head = (1/2)³= 1/8
Point she get = 2*3 - 1 = 5
to score 100 or more point probably she need 160 turns
She has more chances to win but more turns required compared to t=2
let say t = 4
probability of turning head = (1/2)⁴= 1/16
Point she get = 2*4 - 1 = 7
to score 100 or more point probably she need 240 turns
She has less chances to win
for t = 2 she has maximum probability