# statistics problem: there are 20 multiple choice questions on a test and each and 4 possible answers.?

You need 10 right to pass. what s the likelihood if you guess at every questions, you will pass? What is the number of questions you can expect to get correct?

Relevance
• Leltos
Lv 5

Number of questions you expect to get correct = 20/4 = 5

Odds of getting a question wrong = 3/4

Odds of getting a question right = 1/4

Different ways of getting R questions right = 20 C R

Odds of getting R questions right = 20CR * (1/4)^R * (3/4)^(20-R)

Odds of passing = 1 - odds of getting less than 10

Odds of getting 0-9 right (using excel)

= POWER(1/4, X) * POWER(3/4, 20-X) *FACT(20)/FACT(X)/FACT(20-X)

0.003171212

0.021141413

0.066947808

0.133895615

0.189685455

0.202331152

0.168609293

0.112406195

0.060886689

0.027060751

= 0.986135583 chance of failing

Chance of passing = 1 - 0.986135583

= 0.013864

Not very high.

When you guess on a problem that has four choises you have a 1 to 4 chance. So you could get 5 questions right, if you guessed all of em.

probability of getiing it right = 1/4

so you would expect to get 5 right

likelyhood of getting ten right is 1/2 the likely hood of getting 5 right

=(1/4)/2

= 1/8

hope this helps

• Smiles
Lv 4