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

Answer:

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

Step-by-step 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;

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

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)  =  $\binom{7}{7} \times 0.50^{7} \times (1-0.50)^{7-7}$

                        =  $1 \times 0.50^{7} \times 0.50^{0}$

                        =  0.0078