How to found the probability that between 2 and 8 students even, play some sport?

Question

The exercise:

35% of TIP students play sports. Ten students of this institution are randomly chosen, and the discrete random variable

X: number of students, among the 10 selected, who perform some sport.

A) Calculate the probability that at least 4 of them play some sport.

B) Find the probability that between 2 and 8 students even, play some sport.

My solution:

$X$~$Bin(10,0.35)$

a) $P(X\geqslant4) = 1-P(X<4) = 1-P(X\leqslant3) = 1-F_X(3) = 0.6444...$

b) $P(2\leqslant X\leqslant8) = P(X\leqslant8) - P(X\leqslant1) = F_X(8)-F_X(1) = 0.9135...$

This is ok?

Answer 1

Yes both of your solutions are right.

Case 1 -

1 - less than 4 cases.

Case 2 -

Less than equal to 8 - (Case with 0 + Case with 1 student).