The probability that a randomly chosen 5-digit number is made from exactly two digits is :

• $\frac{135}{{10}^4}$

• $\frac{150}{{10}^4}$

• $\frac{134}{{10}^4}$

• $\frac{121}{{10}^4}$

A survey shows that 63% of the peoplein a city read newspaper A whereas 76% read newspaper B. If x% of the people read both the newspapers, then a possible value of x can be :

• 65

• 55

• 37

• 29

Two vertical poles AB = 15m and CD = 10m are standing apart on a horizontal ground with points A and C on the ground. If P is the point of intersection of BC and AD, then the height of P (in m) above the line AC is:

• 10/3

• 6

• 5

• 20/3

In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six. The game stops as soon as either of the players wins. The probability of A winning the game is :

• $\frac{30}{61}$

• $\frac{5}{6}$

• $\frac{5}{31}$

• $\frac{31}{61}$

275.

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is _______

In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is ....

$$\begin{gathered} \mathrm{The} \mathrm{probabilities} \mathrm{of} \mathrm{three} \mathrm{events} \mathrm{A}, \mathrm{B} \mathrm{and} \mathrm{C} \mathrm{are} \mathrm{given} \mathrm{P}\left(\mathrm{A}\right) = 0.6, \mathrm{P}\left(\mathrm{B}\right) = 0.4 \mathrm{and} \\ \mathrm{P}\left(\mathrm{C}\right) = 0.5. \mathrm{If} \mathrm{P}(\mathrm{A} \cup \mathrm{B}) = 0.8, \mathrm{P}(\mathrm{A} \cap \mathrm{C}) = 0.3, \mathrm{P}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C}) = 0.2, \mathrm{P}(\mathrm{B} \cap \mathrm{C})= \mathrm{\beta } \\ \mathrm{and} \mathrm{P}(\mathrm{A} \cup \mathrm{B} \cup \mathrm{C}) = \mathrm{\alpha }, \mathrm{where} 0.85 \le \mathrm{x} \le 0.95, \mathrm{then} \mathrm{\beta } \mathrm{lies} \mathrm{in} \mathrm{the} \mathrm{interval} : \end{gathered}$$

• $\left[0.36, 0.40\right]$

• $\left[0.35, 0.36\right]$

• $\left[0.25, 0.35\right]$

• $\left[0.20, 0.25\right]$

The number of ways of arranging 8 men and 4 women around a circular table such that no two women can sit together is

• 8!

• 4!

• 8!4!

• $7!{}_8\mathrm{P}_4$