Answer to Question #323356 in Statistics and Probability for cherry

Question

Solve the following by using the binomial formula.

1.When rolling a die 100 times, what is the probability rolling a 4 exactly 25 times?

2.       A teacher developed a 5- item multiple choice question with four options in each item. What is the probability of that a certain student who randomly selects his answers will get exactly 4 correct answers?

Answer 1

$P(X=x)=C^{25}_{100}p^x(1-p)^{n-x}$

We have 6 possible results of rolling, and 1 of them is 4. So p=1/6. n=100, x=25

$P(25)=\frac{100!}{25!75!}\times(1/6)^{25}(5/6)^{75}=0.0098$

b.n=5,x=4,p=1/4

$P(4)=\frac{5!}{4!1!}\times(1/4)^4(3/4)^1=5\times(1/256)(3/4)=0.015$