A person throws two fair dice. He wins Rs. 15 for throwing a doublet
( same numbers on the two dice), wins Rs. 12 when the throw results
in the sum of 9 , and loses Rs. 6 for any other outcome on the throw.
Then the expected gain / loss (in Rs.) of the person is :
gain
loss
loss
2 gain
Option 2) 1/4 loss
For initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is then the probability that he is unable to solve less than two problem is :
If the data is such that the mean of first four of these is , the mean of the remaining six is and the sum of squares of all of these is ; then the standard deviation of this data is :
iIf three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equilateral is :
Let a random variable X have a binomial distribution with mean and variance . If , then k is equal to :
If both the mean and the standard deviation of 50 observations
are equal to 16 , then the mean
of is :
400
380
525
480
Minimum number of times a fair coin must be tossed so that
the probability of getting at least one head is more than 99% is :
5
6
8
7
If for some , the frequency distribution of the marks
obtained by 20 students in a test is :
Marks | 2 | 3 | 5 | 7 |
Frequency |
then the mean of the marks is :
3.2
3.0
2.5
2.8
Assume that each born child is equally likely to be a boy or a girl. If two
families have two children each, then the conditional probability that
all children are girls given that at least two are girls is:
The mean and the median of the following ten numbers in increasing order are respectively , then
is equal to :
Four persons can hit a target correctly with probabilities and respectively. If all hit at the target independently, then the probability that the target would be hit,is:
If the standard deviation of the numbers is where then is equal to :
The minimum number of times one has to toss a fair coin so that the probability of observation at least one head is at least 90% is :
A student scores the following marks in five tests : 45,54,41,57,43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is:
The mean and variance of seven observations are , respectively. If of the observations are then the product of the remaining two observations is :
Let and be two non-null events such that . Then, which of the following statements is always correct ?
In a game, a man wins Rs. 100 if he gets 5 or 6 on a throw of a fair die and loses Rs.50 for getting any other number on the die. If he decides to throw the die either till he gets a five or a six or to a maximum of three throws, then his expected gain/loss (in rupees) is :
Let S = {1,2,.........,20}. A subset B of S is said to be ''nice'' , if the sum of the elements of B is 203. Then the probability that a randomly chosen subset of S is ''nice'' is:
A bag contains 30 white balls and 10 red balls. 16 balls are drawn one by one randomly from the bag with replacement. If X be the number of white balls drawn, then is equal to:
4
The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :