probability homework?

Question

This is the question:
a multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses, estimate the probability of getting at least 20% correct.

Answer 1

Dear Clecle,

For this problem you need to use the binomial distribution, which gives the probability of k successes out of N trials as

P(k) = C(N,k) x p^k x (1 - p)^(N - k),
where C(N,k) is the binomial coefficient N! / [k! x (N - k)!].

Here you have p = 0.25 and N = 60. Because the problem wants the probability of at least 20% correct, you will need to use several values for k, then take their sum, as shown below.

Notice that 20% of 60 questions is 12 questions, so you need to find the probability that at least 12 are guessed correctly. You can compute that probability as

P(12) + P(13) + P(14) + . . . + P(60),

or get the same result with fewer terms as

1 - [P(0) + P(1) + P(2) + . . . + P(11)].

Numerically, the binomial distribution with p = 0.25, N = 60, and k = 0, k =1, k = 2, . . . , k = 11 computes approximately as follows.

P(0) = 0.0000000319,
P(1) = 0.0000006378,
P(2) = 0.0000062720,
P(3) = 0.0000404196,
P(4) = 0.0001919931,
P(5) = 0.0007167743,
P(6) = 0.0021901437,
P(7) = 0.0056317980,
P(8) = 0.0124368873,
P(9) = 0.0239525237,
P(10) = 0.0407192903, and
P(11) = 0.0616958945 .

Subtracting their sum from 1 gives the probability of guessing at least 12 questions (20%) correctly:

1 - 0.1475826662
= 0.8524173338 .

Answer 2

She has 9 earnings all. For all dimes, the first %. is a threat of three out of 9 or 3/9 = a million/3. For the 2d %., now there are in undemanding words 8 money left and in undemanding words 2 dimes, so the chance is two/8 or a million/4. For the 0.33 %., there are in undemanding words 7 money left and a million dime, so the chance is a million/7. Now multiply all of those at the same time and also you get: a million/3 x a million/4 x a million/7 = a million/80 4 = 0.0119 For the nickels: First %. 6 nickels out of 9 money = 6/9 = 2/3 2d %. 5 out of 8 = 5/8 0.33 %. is 4 out of seven = 4/7 Multiply those at the same time and also you get: 2/3 x 5/8 x 4/7 = 40/168 = 5/21 = 0.238 So a thanks to do those complications is to make certain the style of possibilities that you want and divide it by ability of the total style of alternatives. once you have not got any replace, you should reduce the total by ability of one after each decision. attempt this in degrees and make certain the chance of each step, then multiply all of them at the same time to get the total chance.

Answer 3

I'm not sure if this is right, but if u have 4^(60*0.2).....
you get 16777216
then multiply it by 60 nCr 12 to find all the possible ways of getting 12 answers correct......
but since it's at least 20%, you'll need to use "1--....."

argh, alas, i've forgotten

Answer 4

some homework can be tricky but some can't be. it depend what the question were giving from the teacher and some teacher can make it a little bit trick to some answer to choose by multiple choice or other way to answer the question.

Answer 5

0.8524173338 .