Sample QuestionsProbability questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In a non$-$leap year, the probability of having $53$ tuesdays or $53$ wednesdays is:
- ✓
$\frac{1}{7}$
- B
$\frac{2}{7}$
- C
$\frac{3}{7}$
- D
Answer: A.
View full solution →Three numbers are chosen from $1$ to $20.$ Find the probability that they are not consecutive:
Answer: B.
View full solution →If the probabilities for $A$ to fail in an examination is $0.2$ and that for $B$ is $0.3,$ then the probability that either $A$ or $B$ fails is:
- A
$>0.5$
- B
$0.5$
- ✓
$\leq0.5$
- D
$0$
Answer: C.
View full solution →Seven persons are to be seated in a row. The probability that two particular persons sit next to each other is:
- A
$\frac{1}{3}$
- B
$\frac{1}{6}$
- ✓
$\frac{2}{7}$
- D
$\frac{1}{2}$
Answer: C.
View full solution →The probability that at least one of the events $A$ and $B$ occurs is $0.6.$ If $A$ and $B$ occur simultaneously with probability $0.2,$ then $\text{P}(\bar{\text{A}})+\text{P}(\bar{\text{B}})$ is:
Answer: C.
View full solution →The probability of an occurrence of event A is 0.7 and that of the occurrence of event B is .3 and the probability of occurrence of both is 0.4
The sum of probabilities of two students getting distinction in their final examinations is 1.2
The probabilities that a typist will make 0, 1, 2, 3, 4, 5 or more mistakes in typing a report are, respectively, 0.12, 0.25, 0.36, 0.14, 0.08, 0.11
The probability of intersection of two events A and B is always less than or equal to those favourable to the event A.
The probability that a student will pass his examination is 0.73, the probability of the student getting a compartment is 0.13, and the probability that the student will either pass or get compartment is 0.96.
If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find:
$\text{P}(\text{A}'\cap\text{B}')$
View full solution →If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find:
$\text{P}(\text{A}\cap\text{B})$
View full solution →If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find:
P(A')
If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find:
$\text{P}(\text{A}\cap\text{B}')$
View full solution →If A and B are mutually exclusive events, P(A) = 0.35 and P(B) = 0.45, find:
$\text{P}(\text{A}\cup\text{B})$
View full solution →An experiment consists of rolling a die until a $2$ appears:
How many elements of the sample space correspond to the event that the $2$ appears on the $k^{th}$ roll of the die?
$[$Hint: First $(k - 1)$ rolls have $5$ outcomes each and $k^{th}$ rolls should result in $1$ outcomes$]$
View full solution →A card is drawn from a deck of 52 cards. Find the probability of getting a king or a heart or a red card.
Suppose an integer from $1$ through $1000$ is chosen at random$,$ find the probability that the integer is a multiple of $2$ or a multiple of $9.$
View full solution →If the letters of the word $\text{ASSASSINATION}$ are arranged at random. Find the Probability that:
No two$ A\ ’s$ are coming together.
View full solution →If the letters of the word ASSASSINATION are arranged at random. Find the Probability that:
Four S’s come consecutively in the word.
If the letters of the word ALGORITHM are arranged at random in a row what is the probability the letters GOR must remain together as a unit?
One urn contains two black balls $($labelled $B_1$ and $B_2)$ and one white ball. $A$ second urn contains one black ball and two white balls $($labelled $W_1$ and $W_2).$ Suppose the following experiment is performed. One of the two urns is chosen at random. Next a ball is randomly chosen from the urn. Then a second ball is chosen at random from the same urn without replacing the first ball:
- Write the sample space showing all possible outcomes.
- What is the probability that two black balls are chosen?
- What is the probability that two balls of opposite colour are chosen?
View full solution →If A and B are two events associated with a random experiment such that P(A) = 0.3, P(B) = 0.2 and $\text{P}(\text{A}\cap\text{B})=0.1,$ then the value of $\text{P}(\text{A}\cap\bar{\text{B}})$ is ____________.
View full solution →Let S = {1, 2, 3, 4, 5, 6} and E = {1, 3, 5}, then $\bar{\text{E}}$is __________.
View full solution →If $e_1, e_2, e_3, e_4$ are the four elementary outcomes in a sample space and $P(e_1) = 0.1, P(e_2) = 0.5, P (e_3) = 0.1,$ then the probability of $e_4$ is ___________.
View full solution →The probability of happening of an event A is 0.5 and that of B is 0.3. If A and B are mutually exclusive events, then the probability of neither A nor B is __________.
The probability that the home team will win an upcoming football game is 0.77, the probability that it will tie the game is 0.08, and the probability that it will lose the game is __________.
Match the following:
| $a.$ |
If $E_1$ and $E_2$ are the two mutually exclusive events |
$i.$ |
$\text{E}_1\cap\text{E}_2=\text{E}_1$ |
| $b.$ |
If $E_1$ and $E_2$ are the mutually exclusive and exhaustive events |
$ii.$ |
$(\text{E}_1-\text{E}_2)\cup(\text{E}_1\cap\text{E}_2)=\text{E}_1$ |
| $c.$ |
If $E_1$ and $E_2$ have common outcomes, then |
$iii.$ |
$\text{E}_1\cap\text{E}_2=\phi,\text{ E}_1\cup\text{E}_2=\text{S}$ |
| $d.$ |
If $E_1$ and $E_2$ are two events such that $\text{E}_1\subset\text{E}_2$ |
$iv.$ |
$\text{E}_1\cap\text{E}_2=\phi$ |
View full solution →Match the proposed probability under Column $C_1$ with the appropriate written description under column $C_2:$
| |
$C_1$ |
|
$C_2$ |
| |
Probability |
|
Written Description. |
| $a.$ |
$0.95$ |
$i.$ |
An incorrect assignment. |
| $b.$ |
$0.02$ |
$ii.$ |
No chance of happening. |
| $c.$ |
$-0.3$ |
$iii.$ |
As much chance of happening as not. |
| $d.$ |
$0.5$ |
$iv.$ |
Very likely to happen. |
| $e.$ |
$0$ |
$v.$ |
Very little chance of happening. |
View full solution →In a large metropolitan area$,$ the probabilities are $87, 36, 30$ that a family $($randomly chosen for a sample survey$)$ owns a colour television set$,$ a black and white television set$,$ or both kinds of sets. What is the probability that a family owns either anyone or both kinds of sets?
View full solution →$A$ sample space consists of $9$ elementary outcomes $e_1, e_2, ...., e_9$ whose probabilities are
$P(e_1) = P(e_2 ) = 0.08, P(e_3 ) = P(e_4) = P(e_5) = 0.1$
$P(e_6) = P(e_7) = 0.2, P(e_8) = P(e_9) = 0.07$
Suppose $A = {e_1, e_5, e_8}, B = {e_2, e_5, e_8, e_9}$
- A
Calculate $P (A), P (B),$ and $\text{P}(\text{A}\cap\text{B})$
- B
Using the addition law of probability$,$ calculate $\text{P}(\text{A}\cup\text{B})$
- C
List the composition of the event $\text{A}\cup\text{B},$ and calculate $\text{P}(\text{A}\cup\text{B})$ by adding the probabilities of the elementary outcomes.
- D
Calculate $\text{P}(\bar{\text{B}})$ from $P(B),$ also calculate $\text{P}(\bar{\text{B}})$ directly from the elementary outcomes of $\bar{\text{B}}$
View full solution →A team of medical students doing their internship have to assist during surgeries at a city hospital. The probabilities of surgeries rated as very complex, complex, routine, simple or very simple are respectively, $0.15, 0.20, 0.31, 0.26, 08.$ Find the probabilities that a particular surgery will be rated:
- A
- B
Neither very complex nor very simple.
- C
- D
View full solution →