Question

Assume that random guesses are made for six multiple choice questions on an SAT​ test, so that there are n equals 6 ​trials, each with probability of success​ (correct) given by p equals 0.6. Find the indicated probability for the number of correct answers. Find the probability that the number x of correct answers is fewer than 4. Upper P left parenthesis Upper X less than 4 right parenthesis equals nothing ​(Round to four decimal places as​ needed.)

Answer 1

Let , X be the number of correct answers.

Here ,

The pmf of X is ,

; x=0,1,2,.....,n and q=1-p

= 0 ; otherwise

Therefore, the indicated probability distribution table is ,

X				P(X=x)
0	1	1	0.004096	0.0041
1	6	0.6	0.01024	0.0369
2	15	0.36	0.0256	0.1382
3	20	0.216	0.064	0.2765
4	15	0.1296	0.16	0.311
5	6	0.07776	0.4	0.1866
6	1	0.046656	1	0.0467

Now ,

P(X<4)=P(X=4)+P(X=3)+P(X=2)+P(X=1)+P(X=0)

=0.3110+0.2765+0.1382+0.0369+0.0041

=0.7667

Therefore , the probability that the number x of correct answers is fewer than 4 is 0.7667.