In a certain gambling game, a player tosses a fair coin; if it falls head, he wins ¢1000. A player with ¢5000 tosses the coin six times. What is the probability that he will be left with ¢6000?
Answers
Given : In a certain gambling game, a player tosses a fair coin; if it falls head, he wins ¢1000. A player with ¢5000 tosses the coin six times.
To find : What is the probability that he will be left with ¢6000?
Solution:
Assuming that he lost 1000¢ if he lose
He starts with 5000
so he can end with 11000 if all 6 wins 0 loss
he can end with 9000 if 5 wins 1 loss
he can end with 7000 if 4 wins 2 loss
he can end with 5000 if 3 wins 3 loss
he can end with 3 000 if 2 wins 4 loss
he can end with 1000 if 1 wins 5 loss
if he lost 5 consecutively then he left no money for 6th toss
He can not end with 6000
so probability = 0
Now assuming that he only win , nothing lost
then he has to win once out of 6 times to win 1000
P(Head ) = 1/2
Probability = ⁶C₁ (1/2)¹(1 - 1/2)⁶⁻¹
= 6/2⁶
= 6/64
= 0.09375
Learn more:
If a coin is tossed one time then the probability of a head is 1/2. If we ...
https://brainly.in/question/13321902
Suppose we have four chests each having two drawers. Chests 1 ...
https://brainly.in/question/15261697