Important Skill?

[kenhung123]

In probability sometimes the question may be really hard but its designed for you to find the probability of the opposite event then do 1-[the probability]. Is this a common skill examiners test? Like the question would take ages if you follow the question as it is given?

[TrueTears]

Well say you have an event A, then the probability of A is given by Pr(A) but the probability of its complement is given by Pr(A') which is equivalent to 1 - Pr(A). You should use this logical relationship to work out the probability of complements if the question wants you to.

[Martoman]

Sure is Kenny.

Say you tossed a coin 78 times. You want to find the probability of at least one head. Now you could calculate:
where X represents a head (or a tail, its the same probability so it won't matter )

OR you can go

So then as an easy application, a question could be of the form ->

You have a biased coin. The chance of it landing on a head is . You throw it times. What is the probability of it landing on heads at least once?
This could easily appear as exam 1, 2 mark question, or the first part of an extended response.

[kenhung123]

Nice, thanks guysssss

[Martoman]

I forgot to post a solution to that.

You want at least 1 head. So you can go 1- Pr(X = 0) (probabilty of all of them being tails)

You know that the probability of heads is 1/n. so probability of tails is 1- (1/n) = (n-1)/n

Now we are ready to solve.

as k is the number of times it is flipped.