An insurance company insured 2000 scooter drivers, 3000 car drivers and 5000 truck drivers. The probabilities that scooter, car and truck drivers meet an accident are 0.02, 0.04, and 0.25 respectively. One of the insured persons meets with an accident. What is the probability that he is a
a) Scooter driver
b) Car driver
Given:
- The number of scooter drivers insured is 2000
- The number of car drivers insured is 3000
- The number of truck drivers insured is 5000
- The probability that a scooter driver meets an accident is 0.02
- The probability that a car driver meets an accident is 0.04
- The probability that a truck driver meets an accident is 0.25
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A player tosses two unbiased coins. He wins Rs. 10 if 2 heads appear, Rs. 5 if one head appears and Rs 1 if no head appears. Find the expected value of the amount won by him.
A person is known to hit the target in 3 out of 4 shots whereas another person is known to hit 2 out of 5 shots. Find the probability that the target being hit when they both try.
An insurance company selected 6000 drivers from a city at random in order to find a relationship between age and accidents. The following table shows the results to these 6000 drivers.
| Age of drivers (in years) Class Interval | Accidents in one year | ||||
| 0 | 1 | 2 | 3 | 4 or more | |
| 18 – 25 | 700 | 310 | 225 | 110 | 85 |
| 25 – 40 | 1100 | 290 | 200 | 105 | 80 |
| 40 – 50 | 1200 | 235 | 175 | 80 | 55 |
| 50 and above | 600 | 205 | 140 | 70 | 35 |
Which of the following statements are true or false? Give reason in support of your answer.
a) When two dice are thrown simultaneously then total number of sample points in the sample space will be 12.
b) Expected value of a continuous random variable X is defined as
E(X) =x f (x)dx
c) If X and Y are independent random variable then V(X – Y) = V(X) – V (Y).
d) If X ~ B(4,3) then variance of X is 12.
e) If probability density function of a normally distributed random variable X is , - ∞ <x< ∞
then variance of X is 36.
An insurance company insured 2000 scooter drivers, 3000 car drivers and 5000 truck drivers. The probabilities that scooter, car and truck drivers meet an accident are 0.02, 0.04, and 0.25 respectively. One of the insured persons meets with an accident. What is the probability that he is a
a) Scooter driver
b) Car driver
If the probability that an individual suffers a bad reaction from an injection of a given serum is 0.002, determine the probability that out of 400 individuals
(i) exactly 2
(ii) more than 3
(iii) at least one
individuals suffer from bad reaction.
Determine the constant k such that the function f(x) = kx2(1-x)2 , 0<x<1 2 is a beta distribution of first kind. Also, find its mean and variance.