Kate and David each have $10. Every time the coin lands on

Question

Kate and David each have $10. Every time the coin lands on heads, Kate gives David $1. Every time the coin lands on tails, David gives tails $1. After 3 tosses, what is the probability that Kate has less than $8?

After 3 tosses, what is the probability that Kate has more than $8?

bmwhype2 · Answer

please correct me if i am wrong

2^3 = 8 total
Lose 3 = 10 - 3 = 7
P(losing 3) = 3C3 = 1
Therefore, 1/8.

======================
8 total
LWW = 10 - 1 + 2 = 11
WWW = 10 + 3 = 13

3C2 = 3
3C3 = 1

3+1 = 4
4/8 = 1/2

eschn3am · Answer

Looks right to me. I'll write it out so we can get a better look at it:

For Kate to have less than $8 she would need to lose $3 and to lose $3 she would need to have 3 heads showing.

 HHH  
HHT
HTH
THH
HTT
THT
TTH
TTT

1/8 scenarios have her losing $3. 1/8 probability she has less than $8


For Kate to have more than $8 she can have anything happen other than 2 or 3 heads.

 HHH
HHT
HTH
THH  
HTT
THT
TTH
TTT

4/8 or 1/2 chance of having more than $8

vscid · Answer

eschn3am,

why cant it be HHT for the second case.
Kate will loose 2 but win one.
doesnt this satisfy the condition that she needs more than 8$ ?

neelesh · Answer

What about WLL = 10+1-2 = 9 ? That is still greater than $8

1/2 is not correct....

neelesh · Answer

This can be solved using binomial probability....

Results of 3 coin tosses:

3 Tails -> Kate = $13
2T, 1H -> Kate = $11
1T, 2H -> Kate = $9
3H -> Kate = $7

We need to find out the probability for more than $8 which is probability of 3T + (2T,1H) + (1T, 2H) as total money has to be >$8

C_3^3*(\frac{1}{2})^3 + C_3^2*(\frac{1}{2})^3 + C_3^1*(\frac{1}{2})^3  -->  \frac{7}{8}

sreehari · Answer

Here is how I have done it -

Kate can't get a final number of $8. It has to be $7 (3 losses), $9 (2 losses, 1 win) etc..

Probability of Kate getting <= $8 is 1/8

So the probability of Kate getting > $8 is 1-1/8 = 7/8.

bmwhype2 · Answer

thanks. wasn't quite sure how to approach this problem.

Kate and David each have $10. Every time the coin lands on

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