Question 1192329: When throwing a coin the chance of it being heads is 0.63. If a person gets heads - they step one step to the right, if tails - one step to the left. What is the probability of being back at the starting point (before making any steps) after 8 throws? What is the probability of being no more than 4 steps away from the starting point after 8 throws?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(53937)   (Show Source):
You can put this solution on YOUR website! .
When throwing a coin the chance of it being heads is 0.63.
If a person gets heads - they step one step to the right, if tails - one step to the left.
(a) What is the probability of being back at the starting point (before making any steps) after 8 throws?
(b) What is the probability of being no more than 4 steps away from the starting point after 8 throws?
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(a) Event (a) is an event having four heads and four tails among the eight throwing the coin.
The experiment throwing a coin is a binomial distribution, so the probability of this event is
P =  =  = 0.206665 (rounded). ANSWER
Solved.
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See the lesson
- Challenging problems on Binomial distribution probability
at this forum.
Answer by greenestamps(13367)  (Show Source):
You can put this solution on YOUR website!
(a) Probability of being back at the starting point after 8 throws.
Do the binomial probability calculation as shown in the response from the other tutor, for the case where there are 4 heads and 4 tails.
(b) Probability of being no more than 4 steps away from the starting point after 8 throws.
(1) Inefficient; but good practice....
In addition to the case above with 4 heads and 4 tails, perform similar binomial calculations for the cases of 6 heads and 2 tails, 5 and 3, 3 and 5, and 2 and 6; and find the sum of the probabilities for all those cases.
(2) A bit less work....
Perform similar binomial probability calculations for the cases of 8 heads and 0 tails, 7 and 1, 1 and 7, and 0 and 8; add those probabilities, and subtract from 1.
Finally, note that if performing these calculations is new to you, it is excellent practice to find the probabilities for all the possible outcomes and verify that the sum of all those probabilities is 1; if that sum is not 1, then there is an error either in your formulas or in the calculations.
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