Question

On a multiple-choice exam with 3 possible answers for each of the 5 questions, find the probability that a student would get 4 or more correct answers just by guessing.

Answer 1

@ganeshie8 @wio @radar

Answer 2

binomial distribution ?

Answer 3

I think so.

Answer 4

just addup the probabilities p(X>=4) = P(4) + P(5)

Answer 5

start by finding the probabiltiy for sucess in guessing a correct answer

Answer 6

So is it P(4)+P(5)=(1/3)^4+(1/3)^5?

Answer 7

thats a good try, but no
P(5) equals (1/3)^5

P(4) is bit tricky as you have a choice to tick false option for any one of the five questions

Answer 8

S : success
F : failure

Answer 9

you can answer exactly four correct answers in any one of below 5 ways
```
FSSSS
SFSSS
SSFSS
SSSFS
SSSSF
```
yes ?

Answer 10

Yes. And then?

Answer 11

Notice each of them have four success ticks and one failure tick
so the probability of each of them is same : (1/3)^4 * (2/3)^1

Answer 12

P(4) = 5 * (1/3)^4 * (2/3)^1

Answer 13

see if that makes sense more or less ^

Answer 14

Yes, it makes sense! Thanks!

Answer 15

yw :) add that to P(5) :

P(X>=4) = P(4) + P(5)
= 5 * (1/3)^4 * (2/3)^1 + (1/3)^5

Answer 16

I did. :)