A and B throw a pair of dice alternately. A wins the game if he gets a total of 9 and B wins if he gets a total of 7. If A starts the game, find the probability of winning the game by B.
A and B throw a pair of dice alternately. A wins the game if he gets a total of 7 and B wins the game if he gets a total of 10. If A starts the game, then find the probability that B wins.
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 ?
If E and F are independent events, then show that
(i) E and F' are independent events.
(ii) E' and F are also independent events.
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.
If A and B are two independent events such that P(A' ∩ B)= 2/15 and P(A ∩ B')= 1/6, then find P(A) and P(B).
If the function f : R → R is given by f(x) = x² + 3x + 1 and g : R → R is given by g(x) = 2x – 3, then find
(i) fog (ii) gof
Form the differential equation of the family of circles in the second quadrant and touching the co-ordinate axes.
Find the points on the curve y = x³ at which the slope of the tangent is equal to y-coordinate of the point.
Find the particular solution of the differential equation given that y = 1, when x = 0.
The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue (marginal revenue). If the total revenue (in rupees) received from the sale of x units of a product is given by R(x) = 3x² + 36x + 5, find the marginal revenue, when x = 5.
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 ?