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 $P(A) = 3/5$ and $P(B) = 1/5$, and $A, B$ are mutually exclusive events, then $P(A \text{ or } B)$ is
2. A card is drawn from a well-shuffled deck of 52 cards. The probability of getting a Spade or an Ace is
3. In a leap year, the probability of having 53 Fridays is
4. Two dice are thrown simultaneously. The probability of getting a total of 9 is
5. If $P(A) = 0.4, P(B) = 0.5$ and $P(A \cap B) = 0.25$, then $P(A \cup B)$ is
6. A coin is tossed twice. If the second throw results in a tail, a die is thrown. Describe the sample space.
7. A bag contains 9 discs of which 4 are red, 3 are blue and 2 are yellow. A disc is drawn at random. Find the probability that it is red or blue.
8. Given $P(A) = 0.5, P(B) = 0.6$ and $P(A \cap B) = 0.3$. Find $P(\text{not A and not B})$.
9. In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that:
   (i) The student opted for NCC or NSS.
   (ii) The student has opted for neither NCC nor NSS.
   (iii) The student has opted for NSS but not NCC.
10. Two dice are thrown. Find the probability of getting an even number on the first die or a total of 8.
11. Three coins are tossed. Consider the events:
    A: 'three heads or three tails'
    B: 'at least two heads'
    C: 'at most two heads'
    Of the pairs (A,B), (A,C) and (B,C), which are independent? Which are mutually exclusive?
12. Case Study: In a relay race, there are 5 teams A, B, C, D, E.
    (i) What is the probability that A, B, C finish first, second and third respectively?
    (ii) What is the probability that A, B, C are the first three to finish (in any order)?
    (iii) What is the probability that A finishes before B?