Question

If Karri takes a 7 question true false test and guess on every question, what is the

probability that she gets all 7 questions correct?

Answer 1

The probability that she gets all 7 questions correct is 0.0078.

Explanation:

We are given that Karri takes a 7 question true-false test and guess on every question.

The above situation can be represented through binomial distribution;

`P(X = r) = \binom{n}{r} * p^(r) * (1-p)^(n-r) ; x = 0,1,2,3,........`

where, n = number of samples (trials) taken = 7 question

r = number of success = all 7 questions correct

p = probability of success which in our question is probability that

question is correct, i.e. p = 50%

Let X = Number of question that are correct

So, X ~ Binom(n = 7, p = 0.50)

Now, the probability that she gets all 7 questions correct is given by = P(X = 7)

P(X = 7) =
`\binom{7}{7} * 0.50^(7) * (1-0.50)^(7-7)`

=
`1 * 0.50^(7) * 0.50^(0)`

= 0.0078