Respuesta :
Answer:
Probability of getting less than all three right is 0.9375.
Step-by-step explanation:
The true-false questions has two options of which only 1 is correct.
P (True-False question correct) = [tex]\frac{1}{2}[/tex]
The multiple-choice question has 4 options of which 1 is correct.
P (Multiple-choice question correct) = [tex]\frac{1}{4}[/tex]
Also provided that the choices are all equally likely and the questions are independent of each other.
Compute the probability that a student gets less than 3 correct answers:
P (Less than 3 correct answers) = 1 - P (All three correct answers)
                           = 1 - [P (First True-False is correct)
                              × P (Second True-False is correct)
                                × P (Multiple choice is correct)]
                           [tex]=1-[\frac{1}{2}\times \frac{1}{2}\times\frac{1}{4}]\\=1-\frac{1}{16}\\ =\frac{15}{16} \\=0.9375[/tex]
Thus, the probability that a student gets less than 3 correct answers is 0.9375.
