A coin toss bet is placed between two friends such that the person who wins four tosses first is the winner. What is the total number of possible ways in which the bet can play out?
Answers
Given : A coin toss bet is placed between two friends such that the person who wins four tosses first is the winner.
To Find : What is the total number of possible ways in which the bet can play out?
Solution:
who wins four tosses first is the winner.
possible cases
7 tosses
6 tosses
5 tosses
4 tosses
We get cases of Win of Head first
4 tosses
All 4 must be Head
Number of ways = 1
5 tosses
5th must be Head
there are 3 Head out of 4 in ⁴C₃ = 4 Ways
6 tosses
6th must be Head
there are 3 Head out of 5 in ⁵C₃ = 10 Ways
7 tosses
7th must be Head
there are 3 Head out of 6 in ⁶C₃ = 20 Ways
Cases of Head wins = 1+ 4 + 10 + 20 = 35
similarly cases when Tails Wins = 35
Total Possible cases = 35 + 35 = 70
70 is total number of possible ways in which the bet can play out.
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Answer:
70
Step-by-step explanation:
Hope this helps