Probability Test

Probability

This is Probability Test-05 for CBSE class 12 Maths.. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
Suppose that two cards are drawn at random from a deck of cards. Let X be the number of aces obtained. Then the value of E(X) is
  • A
    \(\frac{{41}}{{131}}\)
  • B
    \(\frac{2}{{13}}\)
    Correct
  • C
    \(\frac{3}{{13}}\;\)
  • D
    \(\frac{1}{{13}}\;\)
2
Which of the following conditions do Bernoulli trials satisfy?
  • A
    infinite number of dependent trials.
  • B
    finite number of independent trials
    Correct
  • C
    finite number of dependent trials
  • D
    infinite number of independent trials
3
Which of the following conditions do Bernoulli trials satisfy?
  • A
    Each trial has exactly three outcomes: success or failure and the probability of success or failure remains the same in each trial.
  • B
    Each trial has finite number of outcomes and the probability of each outcome remains the same in each trial.
  • C
    Each trial has exactly two outcomes: success or failure and the probability of success or failure remains the same in each trial.
    Correct
  • D
    Each trial has exactly two outcomes: success or failure and the probability of success or failure can vary in each trial.
4
A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of 5 successes?
  • A
    \(\frac{1}{{32}}\;\)
  • B
    \(\frac{3}{{32}}\)
    Correct
  • C
    \(\frac{7}{{32}}\)
  • D
    \(\frac{5}{{32}}\)
5
A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of at least 5 successes?
  • A
    \(\frac{5}{{64}}\;\)
  • B
    \(\frac{7}{{64}}\)
    Correct
  • C
    \(\frac{3}{{64}}\)
  • D
    \(\frac{9}{{64}}\)
6
A die is thrown 6 times. If ‘getting an odd number’ is a success, what is the probability of at most 5 successes?
  • A
    \(\frac{{63}}{{64}}\)
    Correct
  • B
    \(\frac{{37}}{{64}}\)
  • C
    \(\frac{{49}}{{64}}\)
  • D
    \(\frac{{21}}{{64}}\)
7
A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of two successes.
  • A
    \(\frac{{19}}{{216}}\;\)
  • B
    \(\frac{{25}}{{216}}\)
    Correct
  • C
    \(\frac{{41}}{{216}}\)
  • D
    \(\frac{{37}}{{216}}\)
8
Five cards are drawn successively with replacement from a well – shuffled deck of 52 cards. What is the probability that all the five cards are spades?
  • A
    \(\frac{5}{{1024}}\)
  • B
    \(\frac{1}{{1024}}\)
    Correct
  • C
    \(\frac{7}{{1024}}\)
  • D
    \(\frac{3}{{1024}}\)
9
Five cards are drawn successively with replacement from a well – shuffled deck of 52 cards. What is the probability that only 3 cards are spades?
  • A
    \(\frac{{45}}{{512}}\)
    Correct
  • B
    \(\frac{{77}}{{512}}\)
  • C
    \(\frac{{57}}{{512}}\)
  • D
    \(\frac{{41}}{{512}}\)
10
Five cards are drawn successively with replacement from a well – shuffled deck of 52 cards. What is the probability that none is a spade?
  • A
    \(\frac{{243}}{{1024}}\)
    Correct
  • B
    \(\frac{{249}}{{1024}}\)
  • C
    \(\frac{{237}}{{1024}}\)
  • D
    \(\frac{{217}}{{1024}}\)
11
On a multiple choice examination with three possible answers for each of the five questions, what is the probability that a candidate would get four or more correct answers just by guessing ?
  • A
    \(\frac{{17}}{{243}}\)
  • B
    \(\frac{{11}}{{243}}\)
    Correct
  • C
    \(\frac{9}{{243}}\)
  • D
    \(\frac{{13}}{{243}}\)
12
Find the probability of getting 5 exactly twice in 7 throws of a die.
  • A
    \(\frac{7}{{12}}{\left( {\frac{1}{6}} \right)^5}\)
  • B
    \(\frac{7}{{12}}{\left( {\frac{5}{6}} \right)^4}\)
  • C
    \(\frac{5}{{12}}{\left( {\frac{5}{6}} \right)^5}\)
  • D
    \(\frac{7}{{12}}{\left( {\frac{5}{6}} \right)^5}\)
    Correct
13
Find the probability of throwing at most 2 sixes in 6 throws of a single die.
  • A
    \(\frac{{35}}{{18}}\)
  • B
    \(\frac{{35}}{{18}}{\left( {\frac{5}{6}} \right)^4}\)
    Correct
  • C
    \({\left( {\frac{5}{6}} \right)^4}\)
  • D
    \(\frac{{35}}{{19}}{\left( {\frac{5}{6}} \right)^3}\)
14
In a box containing 100 bulbs, 10 are defective. The probability that out of a sample of 5 bulbs, none is defective is
  • A
    \(\frac{9}{{10}}\)
  • B
    \({\left( {\frac{9}{{10}}} \right)^5}\)
    Correct
  • C
    \({\left( {\frac{1}{2}} \right)^5}\)
  • D
    0.1
15
Two numbers are selected at random (without replacement) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find E(X).
  • A
    \(\frac{{10}}{3}\)
  • B
    \(\frac{{11}}{3}\)
  • C
    \(\frac{{16}}{3}\)
  • D
    \(\frac{{14}}{3}\)
    Correct