Question

2.

Answer 1

Answer:

B) 0.02

Step-by-step explanation:

Use the Binomial Theorem

$\displaystyle P(X=x)=\binom{n}{x}p^xq^{n-x}\\\\P(X=4)=\binom{30}{4}(0.30)^4(1-0.30)^{30-4}\\\\P(X=4)=\frac{30!}{4!(30-4)!}(0.30)^4(0.70)^{26}\\ \\P(X=4)=\frac{30!}{4!(26)!}(0.30)^4(0.70)^{26}\\ \\P(X=4)=\frac{30*29*28*27}{4*3*2*1}(0.30)^4(0.70)^{26}\\ \\P(X=4)=27405(0.30)^4(0.70)^{26}\\\\P(X=4)\approx0.0208$

We have the probability of success, $p=0.30$, and the probability of failure, $q=1-0.30=0.70$. The binomial coefficient, $\binom{n}{k}$, represents the amount of possible combinations that $k$ items can be chosen out of $n$ items, with its respective formula $\frac{n!}{k!(n-k)!}$.

Hence, the best choice for the probability that 4 students chosen at random from the class of 30 that want the next test to be on Monday will be option B, 0.02