In a Binomial distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials ?

• $\frac{80}{243}$

• $\frac{40}{243}$

• $\frac{20}{243}$

• $\frac{10}{243}$

The probabilities that a student will solve question A and question B are 0.4 and 0.5 respectively. What is the probability that he solves at least one of the two questions?

• 0.6

• 0.7

• 0.8

• 0.9

Consider the following statements :

$$\begin{gathered} 1. \mathrm{P}\left(\overline{\mathrm{A}} \cup \mathrm{B}\right) = \mathrm{P}\left(\overline{\mathrm{A}}\right) + \mathrm{P}\left(\mathrm{B}\right) - \mathrm{P}\left(\overline{\mathrm{A}} \cap \mathrm{B}\right) \\ 2. \mathrm{P}\left(\mathrm{A} \cap \overline{\mathrm{B}}\right) = \mathrm{P}\left(\mathrm{B}\right) - \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) \\ 3. \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) = \mathrm{P}\left(\mathrm{B}\right)\mathrm{P}\left(\mathrm{A}\overline{)\mathrm{B}}\right) \end{gathered}$$

Which of the above statements are correct ?

• 1 and 2 only

• 1 and 3 only

• 2 and 3 only

• 1, 2 and 3

A train covers the first 5 km of its journey at a speed of 30 km/hr and the next I5 km at a speed of 45 km/hr. What is the average speed of the train ?

• 35km/hr

• 37.5km/hr

• 39.5km/hr

• 40km/hr

$$\begin{gathered} \mathrm{If} \mathrm{A} \mathrm{and} \mathrm{B} \mathrm{are} \mathrm{two} \mathrm{events} \mathrm{such} \mathrm{that} 2\mathrm{P}\left(\mathrm{A}\right) = 3\mathrm{P}\left(\mathrm{B}\right), \mathrm{where} 0 < \mathrm{P}\left(\mathrm{A}\right) < \mathrm{P}\left(\mathrm{B}\right) < 1, \\ \mathrm{then} \mathrm{which} \mathrm{one} \mathrm{of} \mathrm{the} \mathrm{following} \mathrm{is} \mathrm{correct} ? \end{gathered}$$

• $\mathrm{P}\left(\mathrm{A}\overline{)\mathrm{B}}\right) < \mathrm{P}\left(\mathrm{B}\overline{)\mathrm{A}}\right) < \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right)$

• $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) < \mathrm{P}\left(\mathrm{B}\overline{)\mathrm{A}}\right) < \mathrm{P}\left(\mathrm{A}\overline{)\mathrm{B}}\right)$

• $\mathrm{P}\left(\mathrm{B}\overline{)\mathrm{A}}\right) < \mathrm{P}\left(\mathrm{A}\overline{)\mathrm{B}}\right) < \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right)$

• $\mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) < \mathrm{P}\left(\mathrm{A}\overline{)\mathrm{B}}\right) < \mathrm{P}\left(\mathrm{B}\overline{)\mathrm{A}}\right)$

A box has ten chits numbered 0, 1, 2, 3, ..., 9. First, one chit is drawn at random and kept a side. From the remaining, a second chit is drawn at random. What is the probability that the second chit drawn is "9" ?

• $\frac{1}{10}$

• $\frac{1}{9}$

• $\frac{1}{90}$

• None of the above

Two fair dice are rolled. What is the probability of getting a sum of 7 ?

• $\frac{1}{36}$

• $\frac{1}{6}$

• $\frac{7}{12}$

• $\frac{5}{12}$

One bag contains 3 white and 2 black balls, another bag contains 5 white and 3 black balls, If a bag is chosen at random and a ball is drawn from it, what is the chance that it is white ?

• $\frac{3}{8}$

• $\frac{49}{80}$

• $\frac{8}{13}$

• $\frac{1}{2}$

29.

$$\begin{gathered} \mathrm{Consider} \mathrm{the} \mathrm{following} \mathrm{in} \mathrm{respect} \mathrm{of} \mathrm{two} \mathrm{events} \mathrm{A} \mathrm{and} \mathrm{B} : \\ 1. \mathrm{P}(\mathrm{A} \mathrm{occurs} \mathrm{but} \mathrm{not}) = \mathrm{P}\left(\mathrm{A}\right) - \mathrm{P}\left(\mathrm{B}\right) \mathrm{if} \mathrm{B} \subset \mathrm{A} \\ 2. \mathrm{P}(\mathrm{A} \mathrm{alone} \mathrm{or} \mathrm{B} \mathrm{alone} \mathrm{occurs}) = \mathrm{P}\left(\mathrm{A}\right) + \mathrm{P}\left(\mathrm{B}\right) - \mathrm{P}(\mathrm{A} \cap \mathrm{B}) \\ 3. \mathrm{P}(\mathrm{A} \mathrm{U} \mathrm{B}) = \mathrm{P}\left(\mathrm{A}\right) + \mathrm{P}\left(\mathrm{B}\right) \mathrm{if} \mathrm{A} \mathrm{and} \mathrm{B} \mathrm{are} \mathrm{mutually} \mathrm{exclusive} \\ \mathrm{Which} \mathrm{of} \mathrm{the} \mathrm{above} \mathrm{is}/\mathrm{are} \mathrm{correct} ? \end{gathered}$$

• 1 only

• 1 and 3 only

• 2 and 3 only

• 1 and 2 only

A committee of three has to be chosen from a group of 4 men and 5 women. If the selection is made atrandom, what is the probability that exactly two members are men 

• $\frac{5}{14}$

• $\frac{1}{21}$

• $\frac{3}{14}$

• $\frac{8}{21}$