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Probability Maths - Probability

Uttarakhand Board (UBSE) - STD 12 Science - Maths (Uttarakhand - English Medium). 285 questions in this chapter.

Question types

Probability question types

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

285
Questions
5
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 1M.C.Q (1 Marks)1 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 2M.C.Q (1 Marks)1 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
    $\frac{18}{108}$
  • ✓
    $\frac{30}{108}$
  • D
    $\frac{48}{108}$

Answer: C.

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Q 3M.C.Q (1 Marks)1 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 4M.C.Q (1 Marks)1 Mark
A die is thrown and a card is selected ar random from a deck $\text{pf}\ 52$ 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 5M.C.Q (1 Marks)1 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 82 Marks Questions2 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 92 Marks Questions2 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 102 Marks Questions2 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 122 Marks Questions2 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 133 Marks Question3 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 153 Marks Question3 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 163 Marks Question3 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 173 Marks Question3 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 185 Marks Questions5 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 $d_1, 2100$ has disease $d _2$, and others had disease $d _3 .1500$ patients with disease $d _1, 1200$ patients with disease $d _2$, 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 195 Marks Questions5 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 205 Marks Questions5 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 215 Marks Questions5 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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