Questions covered in Standard

Review the question prompts below before starting the timed test. Try each problem independently, then use the interactive test to record your answers and review the worked solutions.

1. If $A$ and $B$ are mutually exclusive events such that $P(A) = 0.3$ and $P(B) = 0.4$, then $P(A \text{ or } B)$ is
2. The variance of the first $n$ natural numbers is
3. In a leap year, the probability of having 53 Sundays is
4. If the coefficient of variation is 50 and the mean is 20, then the standard deviation is
5. A card is drawn from a well-shuffled deck of 52 cards. The probability that it is a King or a Queen is
6. Find the mean deviation about the median for the data: 3, 9, 5, 3, 12, 10, 18, 4, 7, 19, 21.
7. Two dice are thrown simultaneously. Find the probability of getting a sum which is a multiple of 3.
8. If $P(A) = 3/5$ and $P(B) = 1/5$, find $P(A \text{ or } B)$ if A and B are independent events.
9. Find the mean and variance of the data: 6, 7, 10, 12, 13, 4, 8, 12.
10. A committee of 2 persons is selected from 2 men and 2 women. Find the probability that the committee will have (a) no man (b) one man (c) two men.
11. Calculate the Mean and Standard Deviation for the following distribution:
    Class: 0-10, 10-20, 20-30, 30-40, 40-50
    Frequency: 5, 8, 15, 16, 6
12. Case Study: In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. One student is selected at random.
    (i) Find the probability that the student opted for NCC or NSS.
    (ii) Find the probability that the student opted for neither NCC nor NSS.
    (iii) Find the probability that the student opted for NSS but not NCC.