Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the expected value for the number of kings.
Let (X) be the random variable denoting the number of kings obtained in two successive draws with replacement from a well-shuffled pack of 52 cards. On each draw, the probability __________ _____ _____ ______ __________ _______.
_______ _____ ___ __________ ___.
________ ___ __________ ____ ________ ________.
_______ _______ _____ ______ ___ ____ _______ ________ _________.
_________ ____ __________ ________ ________ _____ _______ ______ ___ _______ _______ __________.
___ ____ _________ _______ _____ __________ _________ _____ _________ _______.
___ _______ ________ ____ _______ ___ ___ ______ _____ ______ _________.
___ _______ ______ ________ __________.
_______ ___ __________ __________ __________ ___.
__________ ______ _______ _____ _____.
____ ____ ____ ________ ____ _____ ________ __________ ___ ___.
_______ ___ ______ ___ _________ __________ _______ _____.
__________ _______ ___ ___ ______ ______ _________ ______ ________ ___ ____ ______.
______ __________ _______ ____ ___ ________ _______ ___.
__________ _________ ________ _______ _____ _______.
__________.
Get Full Answer on WhatsApp
Four coins were tossed and number of heads noted. The experiment is repeated 200 times. The number of tosses showing 0, 1, 2, 3 and 4 heads were found distributed as under. Fit a binomial distribution to these observed results assuming that the nature of the coins is not known.
| Number of Heads | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| Number of Tosses | 15 | 35 | 90 | 40 | 20 |
A factory produces certain type of output by 3 machines. The respective daily production figures are- machine X : 4500 units, machine Y: 2000 units and machine Z: 3500 units. Past experience shows that 2% of the output produced by machine X is defective. The corresponding fractions of defectives for the other two machines are 5 and 10 percent respectively. An item is drawn from the day's production. If the drawn item is found to be defective, what is the probability that it has been produced by machine Y?
State whether the following statements are True or False. Give a reason in support of your answer.
(a) If events A, B and C are three mutually exclusive and exhaustive events, then it is possible that ,
and
.
(b) If X is a discrete random variable, then X cannot take countably infinite values.
(c) If X is a standard normal variate, then .
(d) If random variables X and Y follow Bernoulli distributions with parameters 1/2 and 1/3 respectively then the random variable X + Y also follows a Bernoulli distribution with parameter 5/6.
If a problem is randomly selected from a particular book, then probability that students A, B and C can solve the problem are 1/2, 1/3 and 1/4 respectively. If a problem is selected randomly from this book and given to the students A, B and C then what is the probability that problem is solved. They solve the problem independently.
Two cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the expected value for the number of kings.
Three unbiased coins are tossed simultaneously. In which of the following cases are the events A and B independent?
(i) A be the event of getting exactly one tail
B be the event of getting exactly one head
(ii) A be the event that first coin shows tail
B be the event that third coin shows head
Find the probability that a third child in a family is the family's second daughter, assuming the male and female are equally probable.