The probability that a student passes only in Mathematics is \(\frac{1}{3}\).The probability that the student passes only in English is \(\frac{4}{9}\).The probability that the student passes in both of these subjects \(\frac{1}{6}\).The probability that the student will pass in at least one of these two subjects is
- \( \frac{17}{18}\)
- \( \frac{11}{18}\)
- \( \frac{14}{18}\)
- \( \frac{1}{18}\)
The Correct Option is A
Solution and Explanation
Top Questions on Conditional Probability
- A bag contains 19 unbiased coins and one coin with heads on both sides. One coin is drawn at random and tossed, and heads turns up. If the probability that the drawn coin was unbiased is $ \frac{m}{n} $, where $ \gcd(m, n) = 1 $, then $ n^2 - m^2 $ is equal to:
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Given three identical bags each containing 10 balls, whose colours are as follows:
Bag I 3 Red 2 Blue 5 Green Bag II 4 Red 3 Blue 3 Green Bag III 5 Red 1 Blue 4 Green A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from Bag I is $ p $ and if the ball is Green, the probability that it is from Bag III is $ q $, then the value of $ \frac{1}{p} + \frac{1}{q} $ is:
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A gardener wanted to plant vegetables in his garden. Hence he bought 10 seeds of brinjal plant, 12 seeds of cabbage plant, and 8 seeds of radish plant. The shopkeeper assured him of germination probabilities of brinjal, cabbage, and radish to be 25%, 35%, and 40% respectively. But before he could plant the seeds, they got mixed up in the bag and he had to sow them randomly.
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- Probability of event A is 0.7 and event B is 0.4, and $ P(A \cap B^c) = 0.5 $, then the value of $ P(B | A \cup B^c) $ is equal to:
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- \(\text{Let } X \text{ denote the number of hours you play during a randomly selected day. The probability that } X \text{ can take values } x \text{ has the following form, where } c \text{ is some constant:}\)
\(P(X = x) = \begin{cases} 0.1, & \text{if } x = 0 \\ cx, & \text{if } x = 1 \text{ or } x = 2 \\ c(5 - x), & \text{if } x = 3 \text{ or } x = 4 \\ 0, & \text{otherwise} \end{cases}\)
\(\text{Match List-I with List-II:}\)
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Questions Asked in GATE CE exam
Two soils of permeabilities \( k_1 \) and \( k_2 \) are placed in a horizontal flow apparatus, as shown in the figure. For Soil 1, \( L_1 = 50 \, {cm} \), and \( k_1 = 0.055 \, {cm/s} \); for Soil 2, \( L_2 = 30 \, {cm} \), and \( k_2 = 0.035 \, {cm/s} \). The cross-sectional area of the horizontal pipe is 100 cm², and the head difference (\( \Delta h \)) is 150 cm. The discharge (in cm³/s) through the soils is ........ (rounded off to 2 decimal places).
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The most suitable test for measuring the permeability of clayey soils in the laboratory is ___________.
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Consider the beam ACDEB given in the figure. Which of the following statements is/are correct:
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The figures, I, II, and III are parts of a sequence. Which one of the following options comes next in the sequence as IV?
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