Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane is

• 0.06

• 0.14

• 0.2

• 0.2

At a telephone enquiry system, the number of phone cells regarding relevant enquiry follow Poisson distribution with an average of 5 phone calls during 10-minute time intervals. The probability that there is at the most one phone call during a 10-minute time period is

• 6/5

• 5/6

• 6/55

• 6/55

Three houses are available in a locality. Three persons apply for the houses. Each applies to one house without consulting others. The probability that all the three apply for the same house is 

• 2/9

• 1/9

• 8/9

• 8/9

A random variable X has Poisson distribution with mean 2. Then P(X > 1.5) equals

• 2/e²

• 0

• 
• 

Let x₁, x₂, …,x_n be n observations such that  Then a possible value of n among the following is

• 15

• 18

• 19

• 19

A random variable X has the probability distribution:

• 0.87

• 0.77

• 0.35

• 0.35

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

• 37/256

• 219/ 256

• 128/256

• 128/256

A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now a ball is drawn at random from the bag, then the probability that this drawn ball is red, is:

• 3/4

• 3/10

• 2/5

• 1/5

If A, B are two events such that $\mathrm{P}(\mathrm{A} \cup \mathrm{B}) \ge \frac{3}{4} \mathrm{and} \frac{1}{8} \le \mathrm{P}\left(\mathrm{A} \cap \mathrm{B}\right) \le \frac{3}{8}$ then

• $\mathrm{P}\left(\mathrm{A}\right) + \mathrm{P}\left(\mathrm{B}\right) \le \frac{11}{8}$

• $\mathrm{P}\left(\mathrm{A}\right) . \mathrm{P}\left(\mathrm{B}\right) \le \frac{3}{8}$

• $\mathrm{P}\left(\mathrm{A}\right) + \mathrm{P}\left(\mathrm{B}\right) \ge \frac{7}{8}$

• None of the above

If 5 distinct balls are placed at random into 5 cells, then the probability that exactly one cell remains empty, is

• 48/125

• 12/125

• 8/125

• 1/125