Each round Mike and Dean toss coin each. Mike tosses a not fair coin in which the probability to get heads is 0.6. Dean tosses a not fair coin in which the probability to get heads is 0.1. they toss the coins till they get the same results at the same time. What is the probability that there will be at most 5 rounds?

Winston Todd

Winston Todd

Answered question

2022-10-24

Each round Mike and Dean toss coin each. Mike tosses a not fair coin in which the probability to get heads is 0.6. Dean tosses a not fair coin in which the probability to get heads is 0.1. they toss the coins till they get the same results at the same time. What is the probability that there will be at most 5 rounds?

Answer & Explanation

Ramiro Sosa

Ramiro Sosa

Beginner2022-10-25Added 13 answers

Step 1
The game ends when Mike and Dean toss different results.
Mike: Heads = 0.6 + T a i l s = 0.4
Dean: Heads = 0.1 + T a i l s = 0.9
The probability of round being:
Both Heads = 0.60 0.40 = 0.24
Both Tails = 0.10 0.90 = 0.09
Both Same = 0.24 + 0.09 = 0.33
Both Different = 1 0.33 = 0.67
Step 2
What is the probability that of getting to round X?
1 = 100 % (first round is always played)
2 = 0.33 (both same)
3 = 0.33 2 = 0.1089 (both same, twice)
4 = 0.33 3 = 0.0359 (both same, 3x)
5 = 0.33 4 = 0.0118 (both same, 4x)
6 = 0.33 5 = 0.0039 (both same, 5x)
What is the probability that there will be at most 5 rounds?
This is simply 1 minus the probability of getting to round 6
( 1 0.33 5 ) = 0.99608
Winston Todd

Winston Todd

Beginner2022-10-26Added 3 answers

Step 1
The probability till Mike and Dean get the same results at most 5 rounds:
The final results can be...
H H   o r   T T
The probability that Mike and Dean get the same results in a round = 0.6 × 0.1 + ( 1 0.6 ) × ( 1 0.1 ) = 0.42.
Step 2
The probability that Mike and Dean do not get the same results in a round = 1 0.42 = 0.58
Let X be the number of rounds until Mike and Dean get the same results. X G e o ( 0.42 ).
P ( X 5 ) = P ( X = 1 ) + P ( X = 2 ) + P ( X = 3 ) + P ( X = 4 ) + P ( X = 5 )
P ( X 5 ) = 0.42 + 0.58 × 0.42 + ( 0.58 ) 2 × 0.42 + ( 0.58 ) 3 × 0.42 + ( 0.58 ) 4 × 0.42 0.9344   ( c o r r . t o   4   d . p . )

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?