Solutions to Practice Problems for  the Lander Math Contest
Module 11, Solutions (33-35)

33)
The probability of getting exactly 4 heads is equal to:
11C4×(1/2)^11=330/2^11≈0.1611

34) The probability of exactly 3 successful shots is equal to:
9C3×(0.7)^3×(0.3)^6≈0.021

35) Events “at most 3 successful shots” and “at least 2
successful shots” represent all possible outcomes. Thus, P(at
most 3 successful shots) =
=1- P(at least 2 successful shots)=
=1-P(no successful shots) - P(1 successful shot)- P(2
successful shot)=
=1 - 0.3^9 - 9×0.7×0.3^8 - 36×0.7^2×0.3^7 = 0.995709106