Question

A multiple choice has 10 questions. Each question has four answer choices.
what is the probability a student randomly guesses the answers and gets exactly six questions correct?

Answer 1

i think i know how to sove this problem. but im not positive if im correct

Answer 2

he can get exactly 6 questions correct in \(^{10}C_6 \)ways

Answer 3

how would i show work?

Answer 4

and each way has a probability of : \(\large (\frac{1}{4})^6(\frac{3}{4})^4\)

Answer 5

then i got .25^6 * .75^4

Answer 6

and then when i began to simplify further. the decimals didnt seem to make sense to me

Answer 7

so, the total probability for getting "Exactly 6 questions correct" would be :

\(^{10}C_6 \large (\frac{1}{4})^6(\frac{3}{4})^4 \)

Answer 8

isnt that just the equation?

Answer 9

http://www.wolframalpha.com/input/?i=%2810+choose+6%29+%28%5Cfrac%7B1%7D%7B4%7D%29%5E6%28%5Cfrac%7B3%7D%7B4%7D%29%5E4+

Answer 10

so the probability would be 1.62%?

Answer 11

@ganeshie8

Answer 12

probability is always between [0, 1]

Answer 13

so it wouldnt be 1.62?

Answer 14

oh you're saying 1.62 % , then fine :)

Answer 15

so would that be correct?

Answer 16

you're right ! probability is 1.62%

Answer 17

which is same as 0.016

Answer 18

thank you! theres another part of this problem that i need help with

Answer 19

shoot

Answer 20

is getting exactly 10 questions correct the same probability as getting exactly zero correct

Answer 21

1/4 is the probability of getting a question correct
3/4 is the probability of getting a question incorrect

so would i use the same equation from above but replace the 6 with a 10 as well as a 0?

Answer 22

yes u can, but this is realitively easier than that

Answer 23

since randomly picking answers are independent events, u can simply multiply the probabilities

Answer 24

P("getting all 10 questions correct") = \(\large (\frac{1}{4})^{10}\)

Answer 25

P("getting 0 questions correct") = \(\large (\frac{3}{4})^{10}\)

Answer 26

are they same ?

Answer 27

no

Answer 28

i dont believe so

Answer 29

@ganeshie8

Answer 30

correct, so they're not same

Answer 31

okay, and one more part if you dont mind

describe the steps needed to calculate the probability of getting at least six questions correct if the student randomly guesses

Answer 32

atleast 6 questions correct means,
he can get 6 or more question correct, right ?

Answer 33

correct

Answer 34

So,

P("atleast 6 questions correct") = P("Exactly 6 questions correct") + P("Exactly 7 questions correct") + P("Exactly 8 questions correct") + P("Exactly 9 questions correct") + P("Exactly 10 questions correct")

Answer 35

Find the probability for each event
and add them ^^

Answer 36

you dont need to find it literally, just explain in words that... u need to find all probabilities and add them, okay ?

Answer 37

okay thank you !

Answer 38

np.. u wlc :)