CAT4MBA

Q1 A natural number a is chosen at random from the first one hundred natural numbers. What is the probability that a + 100/a > 50?
a. 13/20
b. 3/5
c. 9/20
d. 11/20

Q2. A multiple-choice test consists of five choices per question. You think you know the answer for 75% of the questions and for the other 25% you guess at random. When you think you know the answer, you are right only 80% of the time. Find the probability of getting an arbitrary question right.
a. 0.65
b. 0.05
c. 0.6
d. None of these

Q3. A ball is drawn from a bag which contains 4 balls each of which is equal likely to be a black or a white. If the color of the drawn ball is white then what is the probability that the bag contained 3 white and 1 black ball?
a. 3/7
b. 5/8
c. 3/8
d. 4/7

Q4. Five people entered the lift cabin on the ground floor of an 8-floor building (this includes the ground floor). Suppose each of them, independently and with equal probability, can leave the cabin at any of the other seven floors. Find out the probability of all five people leaving at different floors.
Answer:
a. 360/2401
b. 280/2401
c. 360/2701
d. 280/2701

Direction for Q5 and Q6.
A fair die is tossed twice in succession. Let A denote the first score and B the second score. Consider the quadratic equation
x^2 + Ax + B = 0.
Find the probability that
Q5. The equation has 2 distinct roots.
a. 7/36 b. 17/36 c. 19/36 d. 29/36

Q6. The equation has a double root.
a. 1/18 b. 5/18 b. 7/18 d. 11/18