Probability Test

Probability

This is Probability Test-03 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.
  • A
    \(\frac{{23}}{{102}}\)
  • B
    \(\frac{{29}}{{102}}\)
  • C
    \(\frac{{25}}{{102}}\)
    Correct
  • D
    \(\frac{{27}}{{102}}\)
2
A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.
  • A
    \(\frac{{49}}{{91}}\)
  • B
    \(\frac{{44}}{{91}}\)
    Correct
  • C
    \(\frac{{41}}{{91}}\)
  • D
    \(\frac{{47}}{{91}}\)
3
Given that the events A and B are such that P(A) =\(\frac{1}{2}\), P (A ∪ B) =\(\frac{3}{5}\)and P(B) = p. Find p if they are mutually exclusive
  • A
    \(\frac{1}{{10}}\)
    Correct
  • B
    \(\frac{2}{{10}}\)
  • C
    \(\frac{7}{{10}}\)
  • D
    \(\frac{3}{{10}}\)
4
Given that the events A and B are such that P(A) =\(\frac{1}{2}\), P (A ∪ B) =\(\frac{3}{5}\)and P(B) = p. Find p if they independent.
  • A
    \(\frac{1}{4}\)
  • B
    \(\frac{1}{5}\)
    Correct
  • C
    \(\frac{1}{3}\)
  • D
    \(\frac{1}{2}\)
5
Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4. Find P(A ∩ B)
  • A
    0.15
  • B
    0.14
  • C
    0.10
  • D
    0.12
    Correct
6
Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4.Find P(A ∪ B)
  • A
    0.58
    Correct
  • B
    0.51
  • C
    0.62
  • D
    0.55
7
Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4.Find P (A|B)
  • A
    0.27
  • B
    0.3
    Correct
  • C
    0.2
  • D
    0.33
8
Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4. Find P(B|A).
  • A
    0.5
  • B
    0.2
  • C
    0.3
  • D
    0.4
    Correct
9
If A and B are two events such that P(A) = ¼ , P(B) = ½ and \(P(A \cap B) = \frac{1}{8}\) , Find P(not A and not B ) .
  • A
    3/8
    Correct
  • B
    1/8
  • C
    \(\frac{3}{5}\)
  • D
    \(\frac{2}{5}\)
10
If A and B are two events such that A ⊂ B and P(B) ≠ 0, then which of the following is correct?
  • A
    P(A|B) ≥ P(A)
    Correct
  • B
    P(A|B) < P(A)
  • C
    P(A| B) =\(\frac{{{\text{P}}({\text{B}})}}{{{\text{P}}({\text{A}})}}\)
  • D
    None of these
11
The probability of obtaining an even prime number on each die , when a pair of dice is rolled, is given by :
  • A
    0
  • B
    ½
  • C
    \(\frac{1}{{36}}\)
    Correct
  • D
    \(\frac{1}{3}\)
12
If \({E_1},{\text{ }}{E_2},{\text{ }}...,{\text{ }}{E_n}\) are mutually exclusive and exhaustive events associated with a samplespace, and A is any event of non zero probability, then
  • A
    \(P\left( {{E_i}{\text{|}}A} \right) = \frac{{P\left( {{E_i}} \right)P(A|{E_i})}}{{\mathop \sum \nolimits_{i = 1}^n P\left( {{E_{i - 1}}} \right)P(A|{E_i})}}\)
  • B
    \(P\left( {{E_i}{\text{|}}A} \right) = \frac{{P\left( {{E_i}} \right)P(A|{E_i})}}{{\mathop \sum \nolimits_{i = 1}^n P\left( {{E_i}} \right)P(A|{E_i})}}\)
    Correct
  • C
    \(P\left( {{E_i}{\text{|}}A} \right) = \frac{{P\left( {{E_i}} \right)P(A|{E_i})}}{{\mathop \sum \nolimits_{i = 1}^n P\left( {{E_i}} \right)P(A|{E_{i - 2}})}}\)
  • D
    \(P\left( {{E_i}{\text{|}}A} \right) = \frac{{P\left( {{E_i}} \right)P({E_i}|A)}}{{\mathop \sum \nolimits_{i = 1}^n P\left( {{E_i}} \right)P(A|{E_i})}}\)
13
A bag contains 4 red and 4 black balls, another bag contains 2 red and 6 black balls. One of the two bags is selected at random and a ball is drawn from the bag which is found to be red. Find the probability that the ball is drawn from the first bag.
  • A
    \(\frac{1}{5}\)
  • B
    \(\frac{2}{3}\)
    Correct
  • C
    \(\frac{1}{4}\)
  • D
    \(\frac{1}{3}\)
14
Of the students in a college, it is known that 60% reside in hostel and 40% are day scholars (not residing in hostel). Previous year results report that 30% of all students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an A grade, what is the probability that the student is a hostlier?
  • A
    \(\frac{5}{{13}}\)
  • B
    \(\frac{2}{{13}}\)
  • C
    \(\frac{9}{{13}}\)
    Correct
  • D
    \(\frac{3}{{13}}\)
15
In answering a question on a multiple choice test, a student either knows the answer or guesses. Let \(\frac{3}{4}\)be the probability that he knows the answer and \(\frac{1}{4}\) be the probability that he guesses. Assuming that a student who guesses at the answer will be correct with probability \(\frac{1}{4}\) . What is the probability that the student knows the answer given that he answered it correctly?
  • A
    \(\frac{{11}}{{13}}\)
  • B
    \(\frac{{12}}{{13}}\)
    Correct
  • C
    \(\frac{7}{{13}}\;\)
  • D
    \(\frac{9}{{13}}\)