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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- \(\text{Let } X \text{ denote the number of hours you play during a randomly selected day. The probability that } X \text{ can take values } x \text{ has the following form, where } c \text{ is some constant:}\)
\(P(X = x) = \begin{cases} 0.1, & \text{if } x = 0 \\ cx, & \text{if } x = 1 \text{ or } x = 2 \\ c(5 - x), & \text{if } x = 3 \text{ or } x = 4 \\ 0, & \text{otherwise} \end{cases}\)
\(\text{Match List-I with List-II:}\)
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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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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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