Question

Probability: Nicole is taking a 5-question multiple choice test. If she guesses every answer, and each question has 4 choices, what is the probability that she gets at most one wrong answer?

Answer 1

P(0wrong) + P(1wrong) is part of it ..... kinda fuzzy how to do the rest

wwwr; success= 1/4 , fail = 3/4 per question , hnn

Answer 2

the probability of getting a question wrong seems to me to be: 1/5 * 3/4 = 3/20

Answer 3

the answer sheet says .015625 ):

Answer 4

wwwww

wwwwr
wwwrw
wwrww
wrwww
rwwww

wwwrr
wwrwr
wrwwr

1,5,10,10,5,1 = 32 possible outcomes


rrrrr = 1 possibility
rrrrw = 5 possibilities

so maybe 6/32 has a role in there

Answer 5

im so confused ):

Answer 6

can you refresh my memory any, how did you try to work it?

Answer 7

i used the formula nCr(p)^r(q)^n-r

Answer 8

n=20 right? r = 0 or 1

Answer 9

im not sure ): i put 5 for n and yea i got 0 and 1 for r

Answer 10

there are 20 answers in all to choose from; you want the probability of getting 0 wrong + 1 wrong

Answer 11

i see but idk what to do from there ):

Answer 12

lets try that

1(3/4)^0 (1/4)^(20) + 20(3/4)^1 (1/4)^(19)

it aint 20, your 5 is right

1(3/4)^0 (1/4)^(5) + 20(3/4)^1 (1/4)^(4)

http://www.wolframalpha.com/input/?i=1%283%2F4%29%5E0+%281%2F4%29%5E%285%29+%2B+5%283%2F4%29%5E1+%281%2F4%29%5E%284%29

Answer 13

errr, i forgot to change the 20 to a 5 in the post :)

Answer 14

hold on ill try it o:

Answer 15

P(0wrong) = 5C0 w^0 r^5

P(1wrong) = 5C1 w^1 r^4


P(at most 1 wrong) = P(0) + P(1)

Answer 16

im still not getting the answer on the answer key ):

Answer 17

We can reason through this:
P(0 wrong) = P(all right) = (1/4)^5
P(1 wrong) = (3/4)(1/4)^4 but this can happen in 5 different ways

So out solution is (1/4)^5+5(3/4(1/4)^4))

Answer 18

thats what i put in but i dont get the decimal im supposed to ):

Answer 19

(1/4)^5+5(3/4(1/4)^4)) = 1/64 = 0.015625

Answer 20

wait i think i mixed up p and q ! what were they?

Answer 21

Sorry I'm not good at combinatorics so I can't tell you how to do it formally. I just reasoned it out using basic probability

Answer 22

oh its alright, thanks so much tho!!

Answer 23

Glad to help