Question

The probability of taking a step forward by a man is 1/2. Calculate the probability that he has moved to 4 steps forward in 10 steps

Answer 1

Here is your answer !!

Explanation:

Assumption: the probability of remaining still is 1/2 (ie 50/50 he moves forward or doesn’t move).

Assumption: the probability of taking a step is independent of other steps taken/not taken.

Assumption: the question is asking for exactly four steps forward (rather than at least).

This is a simple probability question.

Let’s call steps forward H, and stays the same place T.

First calculate the probability of getting HHHHTTTTTT

P(HHHHTTTTTT) = 0.5^4 * 0.5^6

but, he could take the four steps at any point during the ten moves so we need to know how many combinations (order irrelevant) there are of taking 4 steps in 10 moves.

you could work it out long hand, however the binomial coefficient formula makes it easy. We have ten spots and want to choose 4 which is 10C4.

10C4 = 10!/(4!*6!) = 10*9*8*7/4*3*2*1 = 10*3*7

so we know there are 210 ways of getting 4 H out of ten moves.

now we multiply the probability of happening buy the number of opportunities for it to happen:

= 210 * 0.5^4 * 0.5^6 = 20.51%

note that this is exactly the same for working out the chance of landing exactly 4 heads at any point during 10 coin tosses.

Answer 2

Given: The probability of taking a step forward by a man is 1/2.

To find: the probability that he has moved to 4 steps forward in 10 steps

Solution: Here first we need to assume that the man will surely take a step, either forward or backwards

So we can say that probability of taking a step backwards will be 1/2.

The steps will be like

FFFFBBBBBB

so the total probability of this will be

p = 1/2(4)+ 1/2(6)

these F AND B can be arranged in many ways and their permutations and combinations will be

10C4 = 210

Now, the total probability will be

P = 10C4× ( 1/2(4)+ 1/2(6) )

Therefore, the probability that he has moved to 4 steps forward in 10 steps will be 5×10C4.