Question

help with this one plz
suppose there are three students and each student tosses a coin 10 times. so what is the chance that at least one of the students gets exactly 5 heads.

Answer 1

\(P(\text{at least one .... happens}) = 1 - P(\text{no such thing happens}).\)
In general, this makes computations easier.
You must compute \(1-P(\text{none of the 3 students got exactly 5 heads})=1-(P(A))^3\)
where \(A=\{\text{one student does not get exactly 5} \}\). To compute P(A), use the same trick: P(A)=1-P(it gets exactly 5 heads).

Answer 2

@reemii please guide me how to calculate P(A)

Answer 3

\(P(\text{a student doesn't obtain exactly 5 heads}) = 1 - P(\text{a student obtains exactly 5 heads})\) (in 10 tosses)
So we will compute : \(P(\text{5 heads in 10 tosses})\). A head appears with probability 0.5. Here you are in the situation of a binomial distribution. (\(X\sim\text{Bin}(10,0.5)\) and you want to know \(P(X=k)\)). Now it's just a formula.

Answer 4

oops, first line is P(not 5 heads) = 1 - P(exactly 5 heads).

Answer 5

many thanks fot the explanation :)

Answer 6

0.5715