2. A bag contains 6 white, 4 red and marbles. Three marbles are drawn at random. What is the probability that one marble is red and the other two are white?

A. 1/2 B. 1/12 C. 3/10 D. 7/12

Answer Answer: Option A Explanation: Let S be the sample space. Then,
n(S) = number of ways of drawing 3 marbles out of 10
= 10c3 = (10*9*8)/(3*2*1) =120
Let E = event of drawing 1 red and 2 white marbles
Therefore n(E) = number of ways of drawing 1 red marble out of 4 and 2 white marbles out of 6
=(4c1*6c2) = (4*6*5/2*1) = 60
Therefore P(E) = n(E)/n(S) = 60/120 = 1/2

3. Four different objects 1,2,3 are distributed at random in 4 places. What is the probability that none of the objects occupies the place corresponding to its number?

A. 1/6 B. 1/3 C. 1/2 D. 1

Answer Answer: Option C Explanation: PLACE : 1 2 3 4
Random : 2134, 2143, 2314, 2341, 2413, 2431
None of the objects occupies the place of that number = 2143, 2341, 2413
n(S) = 6, n(E) = 3
P = 3/6 = 1/2

5. An unbiased die is tossed. Find the probability of getting a multiple of 3?

A. 1/3 B. 1/5 C. 1/6 D. 1/8

Answer Answer: Option A Explanation: Here S = {1,2,3,4,5,6}
Let E be the event of getting a multiple of 3.
Then, E = {3,6}
Therefore P(E) = n(E)/n(S) = 2/6 = 1/3