Study Simplify Special — Probability — GSEB 12 Commerce

Q11m

Which event is given by a special subset $\phi$ of the sample space $U$ ?

Q21m

What is the value of $P(A \cap A')$ for events $A$ and $A'$ ?

Q31m

Which of the following options is true for any event of the sample space ?

Q41m

Which of the following options is not true for any two events $A$ and $B$ in the sample space $U$ where $A \subset B$ ?

Q51m

What is the other name of the classical definition of probability?

Q61m

Which of the following statement for probability of elementary events $H$ and $T$ of random experiment of tossing a balanced coin is not true?

Q71m

Which random experiment from the following random experiments has an infinite sample space?

Q81m

If $A \cup A' = U$ then what type of events are $A$ and $A'$ ?

Q91m

If $P(A/B) = P(A)$ and $P(B/A) = P(B)$ then what type of events are $A$ and $B$ ?

Q101m

Two events $A$ and $B$ of a sample space are mutually exclusive. Which of the following will be equal to $P(B - A)$ ?

Q111m

What is the total number of sample points in the sample space formed by throwing three six-faced balanced dice simultaneously?

Q121m

If one number is randomly selected between 1 and 20, what is the probability that the number is a multiple of 5?

Q131m

If events $A$ and $B$ are independent, which of the following options is true?

Q141m

What is the probability of having 5 Thursdays in the month of February in a year which is not a leap year?

Q151m

If $P(A) = 0.4$ and $P(B') = 0.3$ for two independent events $A$ and $B$ of a sample space then state the value of $P(A \cap B)$ .

Q161m

For two events $A$ and $B$ of a samples space, state the event $(A \cap B) \cup (A \cap B')$ .

Q171m

According to the mathematical definition of probability, what is the probability of each outcome among the $n$ outcomes of a random experiment?

Q181m

Give two examples of random experiment.

Q191m

Draw the Venn diagram for $A-B$ , the difference event of $A$ and $B$ .

Q201m

Define an event.

Q211m

Write the sample space of a random experiment of throwing one balanced die and a balanced coin simultaneously.

Q221m

Define conditional probability.

Q231m

State the formula for the probability of occurrence of at least one event out of three events $A$ , $B$ and $C$ .

Q241m

Define independent events.

Q251m

Write the law of multiplication of probability for two independent events $A$ and $B$ in a sample space.

Q261m

Interpret $P(A/B)$ and $P(B/A)$ .

Q271m

When can we say that three events $A$ , $B$ and $C$ in a sample space are exhaustive?

Q281m

Arrange $P(A \cup B), P(A), P(A \cap B), 0, P(A) + P(B)$ in the ascending order.

Q291m

Define :

(1) Random Experiment

(2) Sample Space

(3) Equi-probable Events

(4) Favourable Outcomes

(5) Probability (Mathematical definition)

(6) Probability (Statistical definition)

(7) Impossible Event

(8) Certain Event

Q301m

For two events $A$ and $B$ in a sample space, $A \cap B = \phi$ and $A \cup B = U$ . State the values of $P(A \cap B)$ and $P(A \cup B)$ .

Q311m

If two events $A$ and $B$ in a sample space are independent then state the formula for $P(A \cup B)$ .

Q321m

If $A = \{x \mid 0 < x < 1\}$ and $B = \{x \mid \frac{1}{4} \leq x \leq 3\}$ then find $A \cap B$ .

Q331m

For two independent events $A$ and $B$ , $P(A) = 0.5$ and $P(B) = 0.7$ . Find $P(A' \cap B')$ .

Q341m

If $P(A) = 0.8$ and $P(A \cap B) = 0.25$ , find $P(A - B)$ .

Q351m

If $P(A) = 0.3$ and $P(A \cap B) = 0.03$ , find $P(B/A)$ .

Q361m

If $P(A) = P(B) = K$ for two mutually exclusive events $A$ and $B$ , find $P(A \cup B)$ .

Q371m

If $P(A' \cap B) = 0.45$ and $A \cap B = \phi$ , find $P(B)$ .

Q381m

Two events $A$ and $B$ in a sample space are mutually exclusive and exhaustive. If $P(A) = \frac{1}{3}$ , find $P(B)$ .

Q391m

2% items in a lot are defective. What is the probability that an item randomly selected from this lot is non-defective?

Q401m

State the number of sample points in the random experiment of tossing five balanced coins.

Q411m

State the number of sample points in the random experiment of tossing one balanced coin and two balanced dice simultaneously.

Q421m

Is it possible that $P(A) = 0.7$ and $P(A \cup B) = 0.45$ for two events $A$ and $B$ in a sample space?

Q431m

Two cards are selected one by one with replacement from 52 cards. State the number of elements in the sample space of this random experiment.

Q441m

For two independent events $A$ and $B$ , $P(B/A) = \frac{1}{2}$ and $P(A \cap B) = \frac{1}{5}$ . Find $P(A)$ .

Q451m

1998 tickets out of 2000 tickets do not have a prize. If a person randomly selects one ticket from 2000 tickets then what is the probability that the ticket selected is eligible for prize?

Q463m

Define random experiment with its characteristics.

Q472m

Define sample space. Give an example.

Q482m

What is a finite sample space? Give an example.

Q492m

What is an infinite sample space? Give an example.

Q502m

What is a certain event? Give an example.

Q512m

What is an impossible event? Give an example.

Q522m

What is a complementary event?

Q532m

Define mutually exclusive events with an example.

Q542m

Define exhaustive events with an example.

Q552m

What is the difference between mutually exclusive and exhaustive events?

Q562m

Can two events be both mutually exclusive and exhaustive? Give an example.

Q572m

Define intersection of two events.

Q582m

Define union of two events.

Q592m

Define difference event $A - B$ .

Q602m

State the mathematical (classical) definition of probability.

Q613m

State the three assumptions of the mathematical definition of probability.

Q623m

State the important results about probability.

Q633m

What is the limitation of the mathematical definition of probability?

Q642m

State the Law of Addition of Probability.

Q652m

State the Law of Multiplication of Probability.

Q663m

What is the difference between selection with replacement and selection without replacement?