Probability

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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?

6 Signup and view all the answers

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

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

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

P(E1) + P(E2) + … + P(En) = 1 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(E1) × P(A / E1) + P(E2) × P(A / E2) + … + P(En) × P(A / En) Signup and view all the answers

What is the purpose of Bayes' rule?

To find the probability of a cause given its effect Signup and view all the answers

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

Prior probabilities 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?

5% Signup and view all the answers

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

A1 ∩ A2 = ∅ Signup and view all the answers

What is the characteristic of independent events?

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

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

Exhaustive cases Signup and view all the answers

What is the characteristic of dependent events?

The occurrence of one event affects the occurrence of the other event. Signup and view all the answers

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

Compatible events Signup and view all the answers

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

P(A1) / P(A) 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?

0.5 Signup and view all the answers

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

25/52 Signup and view all the answers

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

P(A) + P(B) 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?

18 C10 × 2C1 × 1/20 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

256 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

$\frac{51}{101}$ 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

$\frac{15}{56}$ 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

$\frac{96}{625}$ 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

0.4 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(Ai)] - ∑[P(Ai ∩ Aj)] + ∑[P(Ai ∩ Aj ∩ Ak)] - ... + (-1)^n-1 P(A1 ∩ A2 ∩ ... ∩ An) 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(A ∩ B) = 0 Signup and view all the answers

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

∑[P(Ai)] Signup and view all the answers

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

P(A) × P(B) × P(C) Signup and view all the answers

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

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

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?

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

What is the characteristic of independent events?

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

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

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

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

What is the purpose of Bayes' rule?

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

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

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

What is the characteristic of independent events?

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

What is the characteristic of dependent events?

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

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

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

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

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

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?

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

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

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

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

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

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)?

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

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

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

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

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