In a school, all the students play at least one of three indoor games-chess, carrom and table tennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess. What can· be the minimum number of students in the school ?

• 123

• 111

• 95

• 63

In a school, all the students play at least one of threeindoor games-chess, carrom and table tennis. 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess. What can be the maximum number of students in the school ?

• 111

• 123

• 125

• 135

From a deck of cards, cards are taken out with replacement. What is the probability that the fourteenth card taken out is an ace?

• $\frac{1}{51}$

• $\frac{4}{51}$

• $\frac{1}{52}$

• $\frac{1}{13}$

$$\begin{gathered} \mathrm{If} \mathrm{A} \mathrm{and} \mathrm{B} \mathrm{are} \mathrm{two} \mathrm{events} \mathrm{such} \mathrm{that} \mathrm{P}\left(\mathrm{A}\right) = 0.5, \mathrm{P}\left(\mathrm{B}\right) = 0.6 \mathrm{AND} \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) = 0.4, \\ \mathrm{then} \mathrm{what} \mathrm{is} \mathrm{P}\left(\overline{\mathrm{A} \cup \mathrm{B}}\right) = ? \end{gathered}$$

• 0.9

• 0.7

• 0.5

• 0.3

A problem is given to three students A, B and C whose probabilities of solving the problem are $\frac{1}{2}, \frac{3}{4} \mathrm{and} \frac{1}{4}$ respectively. What is the probability that the problem will be solved if they all solve the problem independently ?

• $\frac{29}{32}$

• $\frac{27}{32}$

• $\frac{25}{32}$

• $\frac{23}{32}$

A pair of fair dice is rolled. What is the probability that the second dice lands on a higher value than does the first ?

• $\frac{1}{4}$

• $\frac{1}{6}$

• $\frac{5}{12}$

• $\frac{5}{18}$

A fair coin is tossed and an· unbiased dice is rolled together. What is the probability of getting a 2 or 4 or 6 along with head ?

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{1}{4}$

• $\frac{1}{6}$

If A, B, C are three events, then what is the probability that at least two of these events occur together ?

• $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) + \mathrm{P}\left(\mathrm{B} \cap \mathrm{C}\right) + \mathrm{P}\left(\mathrm{C} \cap \mathrm{A}\right)$

• $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) + \mathrm{P}\left(\mathrm{B} \cap \mathrm{C}\right) + \mathrm{P}\left(\mathrm{C} \cap \mathrm{A}\right) - \mathrm{P}\left(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C}\right)$

• $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) + \mathrm{P}\left(\mathrm{B} \cap \mathrm{C}\right) + \mathrm{P}\left(\mathrm{C} \cap \mathrm{A}\right) - 2\mathrm{P}\left(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C}\right)$

• $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) + \mathrm{P}\left(\mathrm{B} \cap \mathrm{C}\right) + \mathrm{P}\left(\mathrm{C} \cap \mathrm{A}\right) - 3\mathrm{P}\left(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C}\right)$

If two variables X and Y are independent, then what is the correlation coefficient between them ?

• 1

•  - 1

• 0

• None of the above

$$\begin{gathered} \mathrm{Two} \mathrm{independent} \mathrm{events} \mathrm{A} \mathrm{and} \mathrm{B} \mathrm{are} \mathrm{such} \mathrm{P}\left(\mathrm{A} \cup \mathrm{B}\right) = \frac{2}{3} \mathrm{and} \\ \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) = \frac{1}{6}. \mathrm{If} \mathrm{P}\left(\mathrm{B}\right) < \mathrm{P}\left(\mathrm{A}\right), \mathrm{Then} \mathrm{what} \mathrm{is} \mathrm{P}\left(\mathrm{B}\right) = ? \end{gathered}$$

• $\frac{1}{4}$

• $\frac{1}{3}$

• $\frac{1}{2}$

• $\frac{1}{6}$