Probability (p-2) - Maharashtra Board STD 11 Commerce / Arts Maths (commerce) Questions - Vidyadip

Question types

Probability (p-2) question types

93 questions across 5 question groups — pick any mix to generate a Maths (commerce) paper with step-by-step answer keys.

93

Questions

5

Question groups

5

Question types

Solve the following Question.(1 Marks)

Solve the Following Question.(2 Marks)

Solve the Following Question.(3 Marks)

Solve the Following Question.(4 Marks)

Solve the Following Question.(5 Marks)

Sample Questions

Probability (p-2) questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1Solve the following Question.(1 Marks)1 Mark

From a group of 2 men $\left(M_1, M_2\right)$ and three women $\left(W_1, W_2, W_3\right)$, two persons are selected. Describe the sample space of the experiment. If $E$ is the event in which one man and one woman are selected, then which are the cases favourable to $E$ ?

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Q 2Solve the following Question.(1 Marks)1 Mark

Two cards are drawn one after the other from a pack of 52 cards with replacement. What is the probability that both the cards are drawn are face cards?

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Q 3Solve the following Question.(1 Marks)1 Mark

If $P(A)=\frac{1}{4}, P(B)=\frac{2}{5}$ and $P(A \cup B)=\frac{1}{2}$. Find the values of the following probabilities.: $P\left(A^{\prime} \cap B^{\prime}\right)$

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Q 4Solve the following Question.(1 Marks)1 Mark

If $P(A)=\frac{1}{4}, P(B)=\frac{2}{5}$ and $P(A \cup B)=\frac{1}{2}$. Find the values of the following probabilities.: $P\left(A^{\prime} \cup B^{\prime}\right)$

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Q 5Solve the following Question.(1 Marks)1 Mark

If $P(A)=\frac{1}{4}, P(B)=\frac{2}{5}$ and $P(A \cup B)=\frac{1}{2}$. Find the values of the following probabilities.: $\mathrm{P}\left(\mathrm{A}^{\prime} \cap \mathrm{B}\right)$

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Q 6Solve the Following Question.(2 Marks)2 Marks

The odds against a certain event are $5: 2$ and the odds in favour of another independent event are $6: 5$. Find the chance that at least one of the events will happen.

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Q 7Solve the Following Question.(2 Marks)2 Marks

$A, B$ and $C$ are mutually exclusive and exhaustive events associated with the random experiment. Find $P(A)$, given that
$P(B)=\frac{3}{2} P(A)$ and $P(C)=\frac{1}{2} P(B)$

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Q 8Solve the Following Question.(2 Marks)2 Marks

A box contains 25 tickets numbered 1 to 25 . Two tickets are drawn at random. What is the probability that the product of the numbers is even?

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Q 9Solve the Following Question.(2 Marks)2 Marks

A number of two digits is formed using the digits $1,2,3, \ldots . . ., 9$. What is the probability that the number so chosen is even and less than 60 ?

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Q 10Solve the Following Question.(2 Marks)2 Marks

Two-thirds of the students in a class are boys and the rest are girls. It is known that the probability of a girl getting first class is 0.25 and that of a boy getting is 0.28 . Find the probability that a student chosen at random will get first class.

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Q 11Solve the Following Question.(3 Marks)3 Marks

The odds against a husband who is 55 years old living till he is 75 is $8: 5$ and it is $4: 3$ against his wife who is now 48 , living till she is 68 . Find the probability that:
1.the couple will be alive 20 years hence
2. at least one of them will be alive 20 years hence.

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Q 12Solve the Following Question.(3 Marks)3 Marks

There are 2 red and 3 black balls in a bag. 3 balls are taken out at random from the bag. Find the probability of getting 2 red and 1 black ball or 1 red and 2 black balls.

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Q 13Solve the Following Question.(3 Marks)3 Marks

A room has 3 sockets for lamps. From a collection of 10 light bulbs, 6 are defective. A person selects 3 at random and puts them in every socket. What is the probability that the room, will be lit?

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Q 14Solve the Following Question.(3 Marks)3 Marks

Three groups of children contain respectively 3 girls and 1 boy, 2 girls and 2 boys and 1 girl and 3 boys. One child is selected at random from each group. What is the chance that the three selected consist of 1 girl and 2 boys?

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Q 15Solve the Following Question.(3 Marks)3 Marks

A bag contains 8 red balls and 5 white balls. Two successive draws of 3 balls each are made without replacement. Find the probability that the first drawing will give 3 white balls and the second drawing will give 3 red balls.

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Q 16Solve the Following Question.(4 Marks)4 Marks

The odds against student $X$ solving a business statistics problem are $8: 6$ and the odds in favour of student $Y$ solving the same problem are $14: 16$:
1.What is the chance that the problem will be solved, if they try independently?
2.What is the probability that neither solves the problem?

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Q 17Solve the Following Question.(4 Marks)4 Marks

In a group of students, there are 3 boys and 4 girls. Four students are to be selected at random from the group. Find the probability that either 3 boys and 1 girl or 3 girls and 1 boy are selected.

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Q 18Solve the Following Question.(4 Marks)4 Marks

A card is drawn from a well-shuffled pack of 52 cards. Find the probability of it being a heart or a queen.

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Q 19Solve the Following Question.(4 Marks)4 Marks

Two dice are thrown together. What is the probability that sum of the numbers on two dice is 5 or the number on the second die is greater than or equal to the number on the first die?

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Q 20Solve the Following Question.(5 Marks)5 Marks

An urn contains four tickets marked with numbers 112, 121, 122, 222, and one ticket is drawn at random. Let $A_i(i=1,2,3)$ be the event that ith digit of the number of the ticket drawn is 1 . Discuss the independence of the events $A_1, A_2$, and $A_3$.

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