A problem in mathematics is given to 4 students A, B, C, D. Their chances of solving the problem, respectively, are 1/3, 1/4, 1/5 and 2/3. What is the probability that
(i) the problem will be solved ?
(ii) at most one of them solve the problem ?
(i) the problem will be solved ?
(ii) at most one of them solve the problem ?
Let
E be the event = A solves the problem
F be the event = B solves the problem
G be the event = C solves the problem
H be the event = D solves the problem 
E be the event = A solves the problem
F be the event = B solves the problem
G be the event = C solves the problem
H be the event = D solves the problem
Probability of solving specific problem independently by A and B are 1/2 and 1/3 respectively. If both try to solve the problem, independently, then find the probability that
(i) the problem is solved
(ii) exactly one of them solves the problem
A box contains 50 bolts and 50 nuts. Half of the bolts and nuts are rusted. If two items are drawn with replacement, what is the probability that either both are rusted or both are bolts.
A couple has 2 children. Find the probability that both are boys, if it is known that
(i) one of them is a boy
(ii) the older child is a boy.
In a school, there are 1,000 students, out of which 380 are girls. Out of 380 girls, 10% of the girls scored highest in GS. What is the probability that a student chosen randomly scored highest in GS given that the chosen student is a girl ?
A speaks truth in 75% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact ? Do you think that statement of B is always true ?
Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls ? Given that :
(i) the youngest is a girl.
(ii) atleast one is a girl.
P speaks truth in 70% of the cases and Q in 80% of the cases. In what percent of cases are they likely to agree
in stating the same fact ?
Show that the relation R in the set N × N defined by (a, b) R (c, d) if a² + d² = b² + c² is an equivalence relation.
Show that f : N → N, given by f(x) = |``x+1, if x is odd x- 1, if x is even is both one-one and onto.``|
The total expenditure (in ₹) required for providing the cheap edition of a book for poor and deserving students is given by R(x) = 3x² + 36x, where x is the number of set of books. If the marginal expenditure is defined as write the marginal expenditure required for 1200 such sets.