Probability (nCr)

DO YOUR OWN D**N WORK

That doesn't help, I am honestly stuck, and it says that people are here to help, if you aren't going to help me then don't reply

People on here are so rude, really I am sorry Well I will try to help you, If I can't get anything I'll let you know.

Hi SerJibblenits

The Probability that Azher, who always walks to work, arrives late on any day is 0.11. Calculate the Probability that, during a period of 20 working days, he is late on exacalty 4 days.

I'll not only show you the working I will also do my best to explain.
First you must understand that this answer assumes that the chance of being late on any day is indepentant of any his timeliness on any other day.

Prob of being late = P(a) = 0.11
Prob of not late = P(a with a bar on the top) = 1 - 0.11 = 0.89
The probability of being late for the first 4 days and then not late for the next 16 days would be 0.11^4 * 0.89^16 = 2.2689 * 10^(-5) (to 5 significant figures)

Trouble is, he might be late on the 2nd, 5th 16th and 19th day
or he might be late on the 10th, 11th, 14th and 20th day etc
You need some way to work out how many combinations of 4 days you can choose from 20 days.
And this formula will do it fo you
20C4 = 4845
(There is an nCr button on your calculator)

So the probability that he will be late on exactly four days will be 20C4 * (0.11^4) * (0.89^16) = 0.1099 (correct to 4 dp)

SerJibblenuts:

The Probability that Azher, who always walks to work, arrives late on any day is 0.11. Calculate the Probability that, during a period of 20 working days, he is late on exacalty 4 days.

SHOW WORKING

using the binomial theory : p(x)=nCx (p)^x (q)^n-x

let the probability of arriving late be P = 0.11

let the probability of not arriving late be q = 1-0.11= 0.89

n=20, x=4

workings
p(x=4) = 20C4 * (0.11)^4 * (0.89)^16
=4845 * (0.0001464) * (0.1549)
p(x=4)=0.11
conclusion : the probability that he comes late in exactly 4 days is 0.1 i.e 1 in every 10 chances