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Probability Maths - Probability

Maharashtra Board - STD 12 Science - Maths (MSBSHSE - English Medium). 283 questions in this chapter.

Question types

Probability question types

283 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

283
Questions
4
Question groups
5
Question types
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.

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
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 followed by red.
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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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