Answer to Question #323355 in Statistics and Probability for chari

Question #323355

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?


1
Expert's answer
2022-04-05T15:28:22-0400

1:p=16XBin(100,16)P(X=25)=C10025(16)25(116)10025=0.009825882:p=0.25XBin(5,0.25)P(X=4)=C540.254(10.25)54=0.01464841:\\p=\frac{1}{6}\\X\sim Bin\left( 100,\frac{1}{6} \right) \\P\left( X=25 \right) =C_{100}^{25}\cdot \left( \frac{1}{6} \right) ^{25}\left( 1-\frac{1}{6} \right) ^{100-25}=0.00982588\\2:\\p=0.25\\X\sim Bin\left( 5,0.25 \right) \\P\left( X=4 \right) =C_{5}^{4}\cdot 0.25^4\cdot \left( 1-0.25 \right) ^{5-4}=0.0146484


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment