Probability
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Questions and Answers

What is the total number of cases favourable to drawing 2 queens from a pack of 52 cards?

  • 4 C 2 (correct)
  • 52 C 2
  • 6 C 2
  • 2 C 4

    • What is the condition for a collection of events to be mutually exclusive?

  • E1 ∪ E2 ∪....∪ En = S
  • Ai ∩ Aj = Φ for i ≠ j (correct)
  • A1 ∪ A2 ∪....∪ An = S
  • P(A1) + P(A2) +.....+ P(An) = 1

    • What is the characteristic of independent events?

  • They are always dependent on each other
  • They are taken from different experiments (correct)
  • They are taken from a single experiment
  • They are always mutually exclusive

    • What is the total number of exhaustive cases in throwing a die?

    <p>6</p> Signup and view all the answers

    What is the property of a mutually exclusive and exhaustive system of events?

    <p>P(A1) + P(A2) +.....+ P(An) = 1</p> Signup and view all the answers

    What is the condition for events E1, E2, …, En to be mutually exclusive and exhaustive?

    <p>P(E1) + P(E2) + … + P(En) = 1</p> Signup and view all the answers

    What is the probability of event A, which occurs with E1 or E2 or … or En, given by?

    <p>P(E1) × P(A / E1) + P(E2) × P(A / E2) + … + P(En) × P(A / En)</p> Signup and view all the answers

    What is the purpose of Bayes' rule?

    <p>To find the probability of a cause given its effect</p> Signup and view all the answers

    What is the term for the probabilities P(Ei), i = 1, 2, …, n?

    <p>Prior probabilities</p> Signup and view all the answers

    What is the probability that the bolt drawn at random is defective, given that it is from machine A?

    <p>5%</p> Signup and view all the answers

    What is the condition for two events to be mutually exclusive?

    <p>A1 ∩ A2 = ∅</p> Signup and view all the answers

    What is the characteristic of independent events?

    <p>The occurrence of one event does not affect the occurrence of the other event.</p> Signup and view all the answers

    What is the term for the total number of possible outcomes of a random experiment in a trial?

    <p>Exhaustive cases</p> Signup and view all the answers

    What is the characteristic of dependent events?

    <p>The occurrence of one event affects the occurrence of the other event.</p> Signup and view all the answers

    What term is used to describe events that are not mutually exclusive?

    <p>Compatible events</p> Signup and view all the answers

    What is the probability of event A1 given that event A has occurred?

    <p>P(A1) / P(A)</p> Signup and view all the answers

    If P(A) = 0.4 and P(A ∩ A1) = 0.2, what is the value of P(A1) given that A has occurred?

    <p>0.5</p> Signup and view all the answers

    What is the probability that the ball was drawn from bag B given that it is red?

    <p>25/52</p> Signup and view all the answers

    If two events A and B are mutually exclusive, what is the probability of their union?

    <p>P(A) + P(B)</p> Signup and view all the answers

    What is the probability that the first 11 draws contain 10 non-defective and one defective article, and the 12th draw contains a defective article?

    <p>18 C10 × 2C1 × 1/20</p> Signup and view all the answers

    If the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is $\frac{81}{256}$, then the total number of possible outcomes is

    <p>256</p> Signup and view all the answers

    If 100 identical coins each with probability $p$ of showing up heads are tossed once, and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of $p$ is

    <p>$\frac{51}{101}$</p> Signup and view all the answers

    If the mean and the variance of a binomial distribution are 4 and 2 respectively, then the probability of 2 successes is

    <p>$\frac{15}{56}$</p> Signup and view all the answers

    A man takes a step forward with probability 0.4 and backward with probability 0.6. The probability that he takes exactly 2 steps forward in 4 steps is

    <p>$\frac{96}{625}$</p> Signup and view all the answers

    If $A$ and $B$ are two events such that $P(A)=0.4$ and $P(B)=0.5$, then the maximum possible value of $P(A\cap B)$ is

    <p>0.4</p> Signup and view all the answers

    If A1, A2, ..., An are n events associated with a random experiment, what is the generalization of the addition theorem for P(A1 ∪ A2 ∪ ... ∪ An)?

    <p>∑[P(Ai)] - ∑[P(Ai ∩ Aj)] + ∑[P(Ai ∩ Aj ∩ Ak)] - ... + (-1)^n-1 P(A1 ∩ A2 ∩ ... ∩ An)</p> Signup and view all the answers

    If A and B are two arbitrary events, what is the condition for them to be mutually exclusive?

    <p>P(A ∩ B) = 0</p> Signup and view all the answers

    What is the upper bound for P(A1 ∪ A2 ∪ ... ∪ An) according to Booley's inequality?

    <p>∑[P(Ai)]</p> Signup and view all the answers

    If A, B, and C are three arbitrary events, what is the probability of their intersection?

    <p>P(A) × P(B) × P(C)</p> Signup and view all the answers

    What is the condition for events E1, E2, ..., En to be mutually exclusive and exhaustive?

    <p>P(E1 ∪ E2 ∪ ... ∪ En) = 1 and P(Ei ∩ Ej) = 0 for i ≠ j</p> Signup and view all the answers

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