Probability Test

Probability

This is Probability Test-02 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
A coin is tossed three times, if E : head on third toss , F : heads on first two tosses. Find P(E|F)
  • A
    \(\frac{2}{3}\)
  • B
    \(\frac{1}{5}\)
  • C
    \(\frac{1}{2}\)
    Correct
  • D
    \(\frac{1}{3}\)
2
A coin is tossed three times, if E : at least two heads , F : at most two heads. Find P(E|F)
  • A
    \(\;\frac{2}{3}\)
  • B
    \(\frac{2}{7}\)
  • C
    \(\frac{2}{5}\)
  • D
    \(\frac{3}{7}\)
    Correct
3
A coin is tossed three times, E : at most two tails , F : at least one tail. Find P(E|F)
  • A
    \(\frac{3}{7}\)
  • B
    \(\frac{2}{7}\)
  • C
    \(\frac{6}{7}\)
    Correct
  • D
    \(\frac{4}{7}\)
4
A black and a red dice are rolled. Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
  • A
    \(\frac{5}{9}\)
  • B
    \(\frac{1}{3}\)
    Correct
  • C
    \(\frac{4}{9}\)
  • D
    \(\frac{2}{3}\)
5
A black and a red dice are rolled. Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
  • A
    \(\frac{7}{9}\)
  • B
    \(\frac{5}{9}\)
  • C
    \(\frac{1}{9}\)
    Correct
  • D
    \(\frac{4}{9}\)
6
An instructor has a question bank consisting of 300 easy True / False questions,200 difficult True / False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple choice question?
  • A
    \(\frac{1}{9}\)
  • B
    \(\frac{4}{9}\)
  • C
    \(\frac{7}{9}\)
  • D
    \(\frac{5}{9}\)
    Correct
7
Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.
  • A
    0
    Correct
  • B
    0.2
  • C
    0.5
  • D
    1
8
If P(A) = \(\frac{1}{2}\), P(B) = 0, then P(A|B) is
  • A
    not defined
    Correct
  • B
    0
  • C
    1
  • D
    \(\frac{1}{2}\)
9
If A and B are events such that P(A|B) = P(B|A), then
  • A
    P(A) = P(B)
    Correct
  • B
    A = B
  • C
    A ⊂ B but A ≠ B
  • D
    A ∩ B = \(\emptyset \)
10
If E and F are independent, then
  • A
    P (E ∩ F) = P (E) P (F)
    Correct
  • B
    P (E ∩ F) = P (E) P (E|F)
  • C
    P (E ∩ F) =P (E ∪ F)
  • D
    P (E ∩ F) = P (E) P (F|E)
11
If E and F are independent, then
  • A
    P (E|F) = P (E), P (F) ≠ 0
    Correct
  • B
    P (E|F) = P (E’), P (F) ≠ 0E’ is complement of E
  • C
    P (E|F) = P (F), P (F) ≠ 0
  • D
    P (E|F) =P (E’∪ F)E’ is complement of E
12
Let (\({E_1},{\text{ }}{E_2},{\text{ }}...,{\text{ }}{E_n}\)) be a partition of a sample space and suppose that each of \({E_1},{\text{ }}{E_2},{\text{ }}...,{\text{ }}{E_n}\) has nonzero probability. Let A be any event associated with S,then
  • A
    P(A) = P(E0) P (A|E1) + P (E1) P (A|E2) + ... + P (En – 1) P(A|En)
  • B
    P(A) = P(E2) P (A|E1) + P (E2) P (A|E2) + ... + P (En) P(A|En)
  • C
    P(A) = P(E1) P (A|E1) + P (E2) P (A|E2) + ... + P (En) P(A|En)
    Correct
  • D
    P(A) = P(E1) P (A|E1) + P (E1) P (A|E2) + ... + P (En) P(A|En)
13
If P(A) =\(\frac{6}{{11}}\), P(B) =\(\frac{5}{{11}}\)and P(A ∪ B) =\(\frac{7}{{11}}.\)find P(A∩B)
  • A
    \(\frac{5}{{17}}\)
  • B
    \(\frac{4}{{13}}\)
  • C
    \(\frac{4}{{11}}\)
    Correct
  • D
    \(\frac{5}{{11}}\)
14
Two events A and B will be independent, if
  • A
    P(A) + P(B) = 1
  • B
    P(A′B′) = [1 – P(A)] [1 – P(B)]
    Correct
  • C
    A and B are mutually exclusive
  • D
    P(A) = P(B)
15
If P(A) = \(\frac{3}{5}\) and P(B) = \(\frac{1}{5}\), find P (A ∩ B) if A and B are independent events.
  • A
    \(\frac{3}{{25}}\)
    Correct
  • B
    \(\frac{4}{{25}}\)
  • C
    \(\frac{8}{{25}}\)
  • D
    \(\frac{7}{{25}}\)