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Probability - ISC Class 12 Mathematics Questions with Answers, Page 4

92 past-paper questions on Probability from ISC Class 12 Mathematics papers (2027-2017), newest first, in full. Questions 61-80 are on this page, 20 to a page. Tap "Show answer" under a question to see its answer.

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2022 · 6 marks · Short answerOpen: In a bolt factory, machines X, Y and Z manufacture 20%, 35% and 45%…
In a bolt factory, machines X, Y and Z manufacture 20%, 35% and 45% respectively of the total output. Of their output 8%, 6% and 5% respectively are defective bolts. One bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured in the machine Y?

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2021 · 6 marks · Short answerOpen: Given three identical Boxes A, B and C, Box A contains 2 gold and 1 silver…
Given three identical Boxes A, B and C, Box A contains 2 gold and 1 silver coin, Box B contains 1 gold and 2 silver coins and Box C contains 3 silver coins. A person chooses a Box at random and takes out a coin. If the coin drawn is of silver, find the probability that it has been drawn from the Box which has the remaining two coins also of silver.

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2021 · 1 mark · MCQOpen: If and , then the value of is:
If $P(A) = \frac{4}{5}$ and $P(A \cap B) = \frac{7}{10}$, then the value of $P(B/A)$ is:
  • (a)$\frac{1}{8}$
  • (b)$\frac{4}{7}$
  • (c)$\frac{5}{7}$
  • (d)$\frac{7}{8}$

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2020 · 6 marks · Short answerOpen: The probability that a bulb produced in a factory will fuse after 150 days of…
The probability that a bulb produced in a factory will fuse after 150 days of use is $0.05$. Find the probability that out of 5 such bulbs:
(i)[1.5]
None will fuse after 150 days of use.
(ii)[1.5]
Not more than one will fuse after 150 days of use.
(iii)[1.5]
More than one will fuse after 150 days of use.
(iv)[1.5]
At least one will fuse after 150 days of use.

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2019 · 6 marks · NumericalOpen: Given three identical Boxes A, B and C, Box A contains 2 gold and 1 silver…
Given three identical Boxes A, B and C, Box A contains 2 gold and 1 silver coin, Box B contains 1 gold and 2 silver coins and Box C contains 3 silver coins. A person chooses a Box at random and takes out a coin. If the coin drawn is of silver, find the probability that it has been drawn from the Box which has the remaining two coins also of silver.

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2018 · 4 marks · Short answerOpen: Let denote the number of hours you study during a randomly selected school day…
Let $X$ denote the number of hours you study during a randomly selected school day. The probability that $X$ can take the values '$x$' has the following form, where '$k$' is some unknown constant. $P(X = x) = \begin{cases} 0.1, & \text{if } x = 0 \\ kx, & \text{if } x = 1 \text{ or } 2 \\ k(5-x), & \text{if } x = 3 \text{ or } 4 \\ 0, & \text{otherwise} \end{cases}$
(a)[1.0]
Find the value of '$k$'.
(b)[3.0]
What is the probability that you study: (i) at least two hours? (ii) exactly two hours? (iii) at most 2 hours?

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