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
For three unbiased coins, the sample space is: [ S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} ] Case (i): * (A) = exactly one tail = ({HTH, HHT, THH}) * (B) = exactly ___ ________ ___ _________ ________ ____.
_____ _________ _____ ___ _________ _____.
_________ ________ ___ _______ ______ ___ _____ _____ ___ __________.
_________ ______ ___ _________ ___ _______ ______ _____.
________ ____ _________ _____ ____ ___ __________ ____.
__________ ____ ________ _______ _____.
_________ ____ _________ _______ ____ ___ _______ ______ _____ ___ ______.
___ ______ ___ ______ _________ ________ ______.
____ __________ __________ _________ __________ ___ _____.
_______ _______ __________ ________ ___ ______ _______ ________ _______ ______ __________ _______.
________ _____ ________ ___ ________ ____ ________ _________ __________ __________ ____.
_____ _________ ______ _____ _______ ____ _____ ____ ________ _______ __________ ____.
_________ __________ _________ ________ ____.
______ _________ ___ _____ _______ ____ ____ ______ _______ ____ ____ __________.
_________ ____ ___ ________ _______ ______ _________ _________ _______ ______ ________.
_________ _______ ______ _________ _______ _____ ____ ________.
_________ __________ ____ _____ _____ __________ ___ ______ _______ ___ ______.
_________ __________ ____ _______ ______ ________ ______ __________ ______ ______ ________ ______.
_________ __________ ___ ____ _______ ________ _________ _______ _________ _______ ___.
_______ _________ __________ __________ _______ ___ _______.
Get Full Answer on WhatsApp
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.
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?
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 |
Find the probability that a third child in a family is the family's second daughter, assuming the male and female are equally probable.
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
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.