IC28 Mock Test Sample 19
This topic explains the basic concepts of probability, including events, sample space, mutually exclusive and independent events, addition and multiplication theorems, and complementary probability. It covers probabilities using cards, dice, coins, and balls from bags. The chapter also explains how probabilities are calculated for combined events such as “at least one,” “either-or,” and “both occurring together.” Examples include survival probabilities, death probabilities, and repeated experiments. The addition theorem is used for mutually exclusive and non-mutually exclusive events, while the multiplication theorem applies to independent events. These concepts form the foundation for actuarial science, statistics, insurance, and risk calculations.
Question 1
If P is the probability of event E, then per (6.3) the probability of complementary event ‘non-E’ is:
a. 1 − P
b. P − 1
c. P²
d. 1/P
Question 2
Probability of 0 means:
a. Certain to occur
b. Cannot happen
c. Likely to happen
d. Equal chance
Question 3
Per Addition Theorem (6.4), if E1 and E2 are mutually exclusive:
a. P(E1 or E2) = P(E1) + P(E2)
b. P(E1 or E2) = P(E1) × P(E2)
c. P(E1 or E2) = P(E1) − P(E2)
d. P(E1 or E2) = 1
Question 4
In Example 1, probability of rolling 1 or 4 on a 6-sided die is:
a. 1/6
b. 2/6 = 1/3
c. 1/2
d. 1/12
Question 5
Per (6.5), for non-mutually exclusive events E1 and E2:
a. P(E1 or E2) = P(E1) + P(E2) − P(E1 and E2)
b. P(E1 or E2) = P(E1) × P(E2)
c. P(E1 or E2) = P(E1) + P(E2)
d. Always = 1
Question 6
In Example 2, probability of drawing king or club from a 52-card pack:
a. 17/52
b. 16/52 = 4/13
c. 13/52
d. 4/52
Question 7
In Example 3, probability of drawing red or black ball from bag (1R, 3B, 4G):
a. 1/8
b. 3/8
c. 4/8 = 1/2
d. 5/8
Question 8
In Example 4, probability of drawing Ace or King or Queen or Jack from a 52-card pack:
a. 1/13
b. 4/13
c. 1/4
d. 16/52 = 4/13
Question 9
Per (6.6) Multiplication Theorem (independent events):
a. P(E1 and E2) = P(E1) + P(E2)
b. P(E1 and E2) = P(E1) × P(E2)
c. P(E1 and E2) = 1
d. P(E1 and E2) = P(E1) − P(E2)
Question 10
For two independent events, the happening of one:
a. Affects the other
b. Does not influence the other
c. Increases its probability
d. Decreases its probability
Question 11
When two dice are thrown, probability of ‘3 on first AND 4 on second’ is:
a. 1/6
b. 1/12
c. 1/36
d. 2/36
Question 12
Per (6.7) general multiplication theorem (events not necessarily independent):
a. P(E1 and E2) = P1 × P2 where P2 is conditional given E1
b. P1 + P2
c. P1 / P2
d. P1 − P2
Question 13
In Example 5, bag has 8 red and 5 white balls. Probability that 1st ball is white and 2nd is red (without replacement):
a. 5/13 × 8/13
b. 5/13 × 8/12 = 40/156
c. 8/13 × 5/13
d. 5/12 × 8/13
Question 14
In Example 6 (1R + 1W in any order), the probability is:
a. 40/156
b. 80/156 = 10/19.5
c. 80/156
d. 60/156
Question 15
In Example 7, P(A dies in 2y)=0.002, P(B dies in 2y)=0.003, P(C dies in 2y)=0.004. P(A and B die, C survives):
a. 0.000005976
b. 0.0000059
c. 0.005976
d. 0.001
Question 16
In Example 8, a coin is thrown twice. Probability of at least one head:
a. 1/2
b. 3/4
c. 1/4
d. 1
Question 17
In Example 9 (deaths in 5 years: 40→0.04, 45→0.06, 50→0.08), the probability that exactly one survives 5 years is approximately:
a. 0.999808
b. 0.009824
c. 0.169792
d. 0.072192
Question 18
In Example 9, the probability that at least one survives 5 years:
a. 0.999808
b. 0.000192
c. 0.96
d. 0.04
Question 19
In Example 9, probability that at least one dies in 5 years:
a. 0.169792
b. 0.830208
c. 0.999808
d. 0.072192
Question 20
In Example 9(d), probability that 40-year-old dies between ages 50 and 55:
a. 0.04
b. 0.072192
c. 0.96
d. 0.06
