Probability - Maharashtra Board STD 12 Maths Questions

Q 1MCQ1 Mark

If $A$ and $B$ are two events such that $\text{P(A)}=\frac{3}{8},\text{P(B)}=\frac{5}{4}.$ and $\text{P}(\text{A}|\text{B})\times\text{P}(\overline{\text{A}}\cap\text{B})$ is equals to.

A
$\frac{2}{5}$
B
$\frac{3}{8}$
C
$\frac{3}{20}$
✓
$\frac{6}{25}$

Answer: D.

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Q 2MCQ1 Mark

A bag contains $5$ brown and $4$ white socks. A man pulls out two socks. The probability that these are of the sane colour is.

A
$\frac{5}{108}$
B
$\frac{18}{108}$
C
$\frac{30}{108}$
✓
$\frac{48}{108}$

Answer: D.

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Q 3MCQ1 Mark

An urn contains $9$ balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is,

✓
$\frac{5}{84}$
B
$\frac{3}{9}$
C
$\frac{3}{7}$
D
$\frac{7}{17}$

Answer: A.

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Q 4MCQ1 Mark

A die is thrown and a card is selected ar random from a deck pf $52$ playing cards. The probability of getting an even number of the die and a spade card is

A
$\frac{1}{2}$
B
$\frac{1}{4}$
✓
$\frac{1}{8}$
D
$\frac{3}{4}$

Answer: C.

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Q 5MCQ1 Mark

Five persone entered the lift cabin on the ground floor of an $8$ floor house. Suppose that each of them independently and with equal probability can leave the cabin at any flor beginning with the first, then the probability of all $5$ persons leaving at different floors is,

✓
$\frac{^{7}\text{P}_5}{7_5}$
B
$\frac{7_5}{^{7}\text{P}_5}$
C
$\frac{6}{^{6}\text{P}_5}$
D
$\frac{^{5}\text{P}_5}{5}$

Answer: A.

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

A bag contains 8 marbles of which 3 are blue and 5 are red. One marble is drawn at random, its cooler is noted and the marble is replaced in the bag. A marble is again drawn from the bag and its colour is noted. Find the probability that the marble will be,
Blue and red in any order.

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

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

If $\text{P(A)}=\frac{6}{11},\text{P(B)}=\frac{5}{11}$ and $\text{P}(\text{A}\cap\text{B})=\frac{7}{11},$ find
$\text{P}\Big(\frac{\text{B}}{\text{A}}\Big)$

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

6 boys and 6 girls sit in a row at random. Find the probability that all the girls sit together.

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

If $\text{P(A)}=\frac{6}{11},\text{P(B)}=\frac{5}{11}$ and $\text{P}(\text{A}\cap\text{B})=\frac{7}{11},$ find
$\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$

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

A dice is thrown twice and the sum of the numbers appearing is observed to be 6. What is the conditional probability that the number 4 has appeared at least once?

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

From a pack of 52 cards, 4 are drawn one by one without replacement. Find the probability that all are aces (or kings).

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

Two coins are tossed once. Find $\text{P}\Big(\frac{\text{A}}{\text{B}}\Big)$ in each of the following:
A = No tail appears,
B = No head appears.

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

Find the chance of drawing 2 white balls in succession from a bag containing 5 red and 7 white balls, the ball first drawn not being replaced.

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

Ten cards numbered 1 through 10 are placed in a box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than 3, what is the probability that it is an even number?

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Q 16Solve the Following Question.(5 Marks)5 Marks

Let $d_1, d_2, d_3$ be three mutually exclusive diseases. Let $S$ be the set of observable symptoms of these diseases. $A$ doctor has the following information from a random sample of 5000 patients: 1800 had disease $\mathrm{d}_1, 2100$ has disease $\mathrm{d}_2$, and others had disease $\mathrm{d}_3 .1500$ patients with disease $\mathrm{d}_1, 1200$ patients with disease $\mathrm{d}_2$, and 900 patients with disease $d_3$ showed the symptom. Which of the diseases is the patient most likely to have?

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Q 17Solve the Following Question.(5 Marks)5 Marks

If A and B are two independent events such that $\text{P}(\overline{\text{A}}\cap\text{B})=\frac{2}{15}$ and $\text{P}(\text{A}\cap\overline{\text{B}})=\frac{1}{6}$, then find P(B).

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Q 18Solve the Following Question.(5 Marks)5 Marks

A and B throw a pair of dice alternately. A wins the game if he gets a total of $7$ and B wins the game if he gets a total of $10$. If A starts the game, then find the probability that B wins.

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Q 19Solve the Following Question.(5 Marks)5 Marks

$A, B$ and $C$ in order toss a coin. The one to throw a head wins. What are their respective chances of winning assuming that the game may continue indefinitely?

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

A and B take turns in throwing two dice, the first to throw 9 being awarded the prize. Show that their chance of winning are in the ratio 9 : 8.

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