Statistics and Probability Answers

(a) A player tosses 3 fair coins. He wins Rs.500 if 3 heads appear, Rs.300 if 2 heads appear, Rs.100 if 1 head occurs. On the other hand, he loses Rs.1500 if 3 tails occur. Find the expected gain of the player and variance

An anti – aircraft gun can take a maximum of 4 shots at an enemy plane moving away from it. The probabilities of hitting the plane at the first, second, third and fourth shot are 0.4, 0.3, 0.2 and 0.1 respectively. The probability that the gun hits the plane is

A pair of dice is rolled 180 times. What is the probability that a total of six occurs
a) At least 30 times b)between 33 and 42 times inclusive. Use Normal approximation to Binomial distribution

(a) A player tosses 3 fair coins. He wins Rs.500 if 3 heads appear, Rs.300 if 2 heads appear, Rs.100 if 1 head occurs. On the other hand, he loses Rs.1500 if 3 tails occur. Find the expected gain of the player and variance.
(b) The trouble shooting capability of an IC chip in a circuit is a random variable X whose distribution function is given by where x denote the number of years. Find the probability that the IC chip will work properly (i) less than 8 years (ii) beyond 8 years (iii) between 5 to 7 years

The error of X of certain physical quantity is decided by the density function

a. Determine k that renders f(x) as a valid density function .
b. Find the probability that a random error in measurement is less than 0.5.
c. Find the probability that magnitude of error exceeds 1.

A box contains 3 red marbles and 7 white marbles. A marble is drawn from the box and the marble is replaced by a marble of the other colour. A second marble is drawn from the box. What is the probability that second marble is red?

3. The Probability that Ram will hit a target is 0.56 and the Probability that Shyam will hit the target is 0.45. The Probability that both will hit the target is 0.25. Find the Probability that
i) at least one will hit the target
ii) exactly one will hit the target
iii) not more than will hit the target

The sales in a two wheeler showroom is exponentially distributed with mean equal to 4. If two days are selected at random, what is the probability that
a) on both days the sales is over 5 units
b) the sale is over 5 units on at least one of the two days.

Three employees E1 ,E2 ,E3 of a software company try for the post of Team Leader. Their chances of succeeding are 4:3:3. The Probability that a certain employee E4 will be given pink slip when E1 ,E2 ,E3 is made Team Leader are 0.3,0.2,0.1 respectively. What is the Probability that E4 will not be given pink slip.

Previous results indicate that 1 in 1000 transistors are defective on average.Without using table,
a)determine the largest number,N,of transistors that can be put in a box so that the probability of acceptable transistors is at least 0.5.