Question

Suppose you had to

guess on a four-choice
multiple-choice test and
were given four questions.
Find the binomial
probability distribution.
( + ) ℎ =
4 = 0.25

Answer 1

For 0 correct answer
`^4c_0p^0q^(4-0)`

For 1 correct answer
`^4c_1p^1q^(4-1)`

For 2 correct answer
`^4c_2p^0q^(4-2)`

For 3 correct answer
`^4c_3p^1q^(4-3)`

For 4 correct answer
`^4c_4p^1q^(4-4)`

Step-by-step explanation:

It is given that there are 4 questions n = 4

Number of choices is 4

So probability of getting correct answer
`=(1)/(4)`

Probability of getting incorrect answer
`=1-(1)/(4)=(3)/(4)`

Probability distribution is given by
`^nc_rp^rq^(n-r)`

Therefore probability distribution of 0 correct answer

`^4c_0p^0q^(4-0)`

Therefore probability distribution of 1 correct answer

`^4c_1p^1q^(4-1)`

Therefore probability distribution of 2 correct answer

`^4c_2p^0q^(4-2)`

Therefore probability distribution of 3 correct answer.

`^4c_3p^1q^(4-3)`

Therefore probability distribution of 4 correct answer.

`^4c_4p^1q^(4-4)`