There are 5 girls and 2 boys, then the probability that no two boys are sitting together for a photograph is
- A$\frac{1}{21}$
- B$\frac{4}{7}$
- C$\frac{2}{7}$
- ✓$\frac{5}{7}$
Answer: D.
View full solution →Question types
Probability question types
306 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
306
Questions
7
Question groups
5
Question types
01
MCQ
194 Q→02Solve the Following Question.(2 Marks)
28 Q→03Solve the Following Question.(3 Marks)
30 Q→04Solve the Following Question.(4 Marks)
31 Q→05Solve the Following Question.(5 Marks)
10 Q→06Answer the following questions in short.
9 Q→07Complete the following activities and rewrite it : (2M)
4 Q→Sample Questions
Probability questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The odds against an event are 5 : 3 and the odds in favour of another independent event are 7 : 5. The probability that at least one of the two events will occur is
- A$\frac{52}{96}$
- ✓$\frac{71}{96}$
- C$\frac{69}{96}$
- D$\frac{13}{96}$
Answer: B.
View full solution →A fair die is tossed twice. What are the odds in favour of getting 4, 5, or 6 on the first toss and 1, 2, 3, or 4 on the second toss?
- A.1:3
- B.3 : 1
- ✓.1 : 2
- D.2 : 1
Answer: C.
View full solution →The bag I contain 3 red and 4 black balls while Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. The probability that it was drawn from Bag II is
- A$\frac{33}{68}$
- B$\frac{35}{69}$
- C$\frac{34}{67}$
- ✓$\frac{35}{68}$
Answer: D.
View full solution →The probability that a student knows the correct answer to a multiple-choice question is
$\frac{2}{3}$. If the student does not know the answer, then the student guesses the answer. Theprobability of the guessed answer being correct is $\frac{1}{4}$. Given that the student has answered
the question correctly, the probability that the student knows the correct answer is
- A$\frac{5}{6}$
- B$\frac{6}{7}$
- C$\frac{7}{8}$
- ✓$\frac{8}{9}$
Answer: D.
View full solution →Suppose that five good fuses and two defective ones have been mixed up. To find the defective fuses, we test them one-by-one, at random and without replacement What is the probability that we are lucky and find both of the defective fuses in the first two tests?
An urn contains 5 red balls and 2 green balls. A ball is drawn. If it’s green, a red ball is added to the urn, and if it’s red, a green ball is added to the urn. (The original ball is not returned to the urn). Then a second ball is drawn. What is the probability that the second ball is red?
A die is loaded in such a way that the probability of the face with j dots turning up is proportional to j for j = 1, 2,….., 6. What is the probability, in one roil of the die, that an odd number of dots will turn up?
A fair die is thrown. What are the odds in favour of getting a number which is a perfect square in uppermost face of die?
Three professors A, B and C appear in an interview for the post of Principal. Their chances of getting selected as a principal are $\frac{2}{9}, \frac{4}{9}, \frac{1}{3}$. The probabilities they introduce new course in the college are $\frac{3}{10}$, $\frac{1}{2}, \frac{4}{5}$ respectively. Find the probability that the new course is introduced.
View full solution →In a factory which manufactures bulbs, machines A, B, and C manufacture respectively 25%, 35% and 40% of the bulbs. Of their outputs, 5, 4, and 2 percent are respectively defective bulbs. A bulb is drawn at random from the product and is found to be defective. What is the probability that it is manufactured by machine B?
Given three identical boxes, I, II, and III, each containing two coins. In box I, both coins are gold coins, in box II, both are silver coins and in box III, there is one gold and one silver coin. A person chooses a box at random and takes out a coin. If the coin is of gold, what is the probability that the other coin in the box is also of gold?
A machine produces parts that are either good (90%), slightly defective (2%), or obviously defective (8%). Produced parts get passed through an automatic inspection machine, which is able to detect any part that is obviously defective and discard it. What is the probability that the quality of the parts that make it through the inspection machine and get shipped?
Find the probability that a year selected will have 53 Wednesdays.
Let $A$ and $B$ be independent events with $P(A)=\frac{1}{4}$ and $P(A \cup B)=2 P(B)-P(A)$. Find
View full solution →(i) P(B)
2. P(A/B)
3. P(B’/A)
A family has two children. One of them is chosen at random and found that the child is a girl. Find the probability that
(i) both the children are girls.
ii. both the children are girls given that at least one of them is a girl.
Consider independent trials consisting of rolling a pair of fair dice, over and over. What is the probability that a sum of 5 appears before a sum of 7?
$A$ and $B$ throw a die alternatively till one of them gets a $3$ and wins the game. Find the respective probabilities of winning. $($Assuming $A$ begins the game$).$
View full solution →The ratio of boys to girls in a college is 3 : 2 and 3 girls out of 500 and 2 boys out of 50 of that college are good singers. A good singer is chosen. What is the probability that the chosen singer is a girl?
The chances of $P, Q$ and $R$, getting selected as principal of a college are $\frac{2}{5}, \frac{2}{5}, \frac{1}{5}$
View full solution →respectively. Their chances of introducing IT in the college are $\frac{1}{2}, \frac{1}{3}, \frac{1}{4}$ respectively. Find
the probability that (a) IT is introduced in the college after one of them is selected as a principal.
B. IT is introduced by Q.
For three events A, B and C, we know that A and C are independent, B and C are
View full solution →independent, $A$ and $B$ are disjoint, $P(A \cup C)=\frac{2}{3}, P(B \cup C)=\frac{3}{4}, P(A \cup B \cup C)=\frac{11}{12}$. Find
P(A), P(B) and P(C).
If $P(A)=P(A / B)=\frac{1}{5}, P(B / A)=\frac{1}{3}$, then find
View full solution →(i) P(A’/B)
The probability that a man who is 45 years old will be alive till he becomes 70 is $\frac{5}{12}$. The
View full solution →probability that his wife who is 40 years old will be alive till she becomes 65 is $\frac{3}{8}$. What is
the probability that, 25 years hence,
the couple will be alive?
(b)exactly one of them will be alive?
(c)none of them will be alive?
(d)at least one of them will be alive?
Two hundred patients who had either Eye surgery or Throat surgery were asked whether they were satisfied or unsatisfied regarding the result of their surgery. The following table summarizes their response.
If one person from the 200 patients is selected at random, determine the probability (a) that the person was satisfied given that the person had Throat surgery.
2.that person was unsatisfied given that the person had eye surgery.
3.the person had Throat surgery given that the person was unsatisfied.
The probability that a student $X$ solves a problem in dynamics is $\frac{2}{5}$ and the probability that
View full solution →student $Y$ solves the same problem is $\frac{1}{4}$. What is the probability that
i. the problem is not solved?
ii. the problem is solved?
iii. the problem is solved exactly by one of them?
Find the probability that a single toss of a die will result in a number less than 4 if it is given that the toss resulted in an odd number.
Sunita and Samrudhi who live in Mumbai wish to go on holiday to Delhi together. They can travel to Delhi from Mumbai either by car or by train or plane and on reaching Delhi they can go for city-tour either by bus or Taxi. Describe the sample space, showing all the combined outcomes of different ways they could complete city-tour from Mumbai.
Describe the sample space of the experiment when a coin and a die are thrown simultaneously.
Let $S=$ Set of all positive integers not exceeding 50 ;
Event $ A=$ Set of elements of $S$ that are divisible by 6 ; and
Event $\mathrm{B}=$ Set of elements of $\mathrm{S}$ that are divisible by 9 . Find $A \cup B$
View full solution →Event $ A=$ Set of elements of $S$ that are divisible by 6 ; and
Event $\mathrm{B}=$ Set of elements of $\mathrm{S}$ that are divisible by 9 . Find $A \cup B$
If odds in favour of X solving a problem are 4 : 3 and odds against Y solving the same problem are 2 : 3. Find the probability of: Y solving the problem
If $A$ and $B$ are two independent events and $P(A)=\frac{3}{5}, P(B)=\frac{2}{3}$, find
i) $\mathrm{P}(\mathrm{A} \cap \mathrm{B})$ ii) $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)$ iii) $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)$ iv) $P\left(A^{\prime} \cap B^{\prime}\right)$ v) $P(A \cup B)$
View full solution →i) $\mathrm{P}(\mathrm{A} \cap \mathrm{B})$ ii) $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}^{\prime}\right)$ iii) $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)$ iv) $P\left(A^{\prime} \cap B^{\prime}\right)$ v) $P(A \cup B)$
Two dice are thrown together. What is the probability that,
i) Sum of the numbers is divisible by 3 or 4?
ii) Sum of the numbers is neither divisible by 3 nor 5?
i) Sum of the numbers is divisible by 3 or 4?
ii) Sum of the numbers is neither divisible by 3 nor 5?
The letters of the word STORY be arranged randomly. Find the probability that
a) T and Y are together.
b) arrangment begins with T and end with Y.
a) T and Y are together.
b) arrangment begins with T and end with Y.
If A∪B∪C = S (the sample space) and A, B and C are mutually exclusive events, can the
following represent probability assignment?
i) P(A) = 0.2, P(B) = 0.7, P(C) = 0.1
ii) P(A) = 0.4, P(B) = 0.6, P(C) = 0.2
following represent probability assignment?
i) P(A) = 0.2, P(B) = 0.7, P(C) = 0.1
ii) P(A) = 0.4, P(B) = 0.6, P(C) = 0.2
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