# Thread: Probability question. Pi = ??

1. ## Probability question. Pi = ?? and also..

Q: It is noted that 8% of abc students are left handed, if 20 students are randomly selected, calculate

Probability that none of them are left handed.

For this, my pi is 0.08 or 0.92?'

and also

Q: Do you agree that " if two events are mutually exclusive then these two events will be independent"? why?

I know that mutually exclusive events means if event A happens, then Event B cannot happen, vice-versa.

and independent events are events that do not affect the outcome of another.

but how to put it in words as my English is not too good.

2. ## Re: Probability question. Pi = ??

If 8% of the student population is left-handed, this means the probability of a randomly selected student not being left-handed is given by P = 1–0.08 = 0.92. Since all twenty randomly selected students should not be left-handed, the probability is then given by P = 0.92×0.92×0.92×…×0.92 (to 20 terms) ≈ 0.1887.

3. ## Re: Probability question. Pi = ??

Originally Posted by Con-Tester
If 8% of the student population is left-handed, this means the probability of a randomly selected student not being left-handed is given by P = 1–0.08 = 0.92. Since all twenty randomly selected students should not be left-handed, the probability is then given by P = 0.92×0.92×0.92×…×0.92 (to 20 terms) ≈ 0.1887.
but for my presentation of working, should it be 20C0 X 0.08^0 X (1-0.08)^20-0?
Which also gets 0.1887.

4. ## Re: Probability question. Pi = ??

There are many ways to get a probability, especially since you can always use compliments.

5. ## Re: Probability question. Pi = ??

Originally Posted by tiochaota
but for my presentation of working, should it be 20C0 X 0.08^0 X (1-0.08)^20-0?
Which also gets 0.1887.
Sure, if you feel you have to use the full binomial formula. If you work it all out, 20C0 = 1, 0.08^0 = 1 and (1–0.08)^(20–0) = 0.92^20, giving P = 1×1×0.92^20 = 0.92^20 = 0.92×0.92×0.92×…×0.92 (to 20 terms) — i.e., the same answer I gave.

My point here is that it’s fine if you want to learn the formula by rote, but my view is that a deeper understanding of probability is obtained when applying counting rules and/or pigeonhole principles whenever possible.