The principal will randomly choose 6 students from a large school to represent the school in a newspaper photograph. The probability that a chosen student is an athlete is 30% (assume that this doesn't change). What is the probability that 4 athletes are chosen? What is the probability that at least 4 athletes are chosen?

by "large" i guess we are to assume it is infinitely large so the probability that any one athlete is chosen is always \(0.3\)

therefore the probability that 4 athletes are chosen is \[\binom{6}{4}(0.3)^4(0.7)^2\] the binomial probability

maybe you have seen \(\binom{6}{4}\) written as \(_6C_4\) or "six choose 4" compute via \[\binom{6}{4}=\frac{6\times 5}{2}=3\times 5=15\] the rest requires a calculator

Thanks, but what would I do for at least four athletes chosen?

at least four is a pita you have to compute 4, 5 or 6 and add them up

\[15(0.3)^4(0.7)^2+6(0.3)^5(0.7)+(0.3)^6\] in other words

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