The chance of an event happening is the square of the chance of a second event but the odds against the first are the cube of the odds against the second. The chances of the events are

Of three independent events, the chance that only the first occurs is a , the chance that only the second occurs is b , and the chance of only the third is c . Show that the chances of three events are respectively, a/(a+x),b/(b+x),c/(c+x) where x is a root of the equation (a+x)(b+x)(c+x)=x^2

If the probability of non-occurrence of an event is (4)/(7) then the odds against the event are -

If the odds against an event are 4 : 5, then the probability of occurrence of the events is -

An unbiased die is thrown twice. Let the event A be "odd number on the first throw" and B the event "odd number on the second throw". Check the independence of the events A and B.

If the odds against an event are 4:5, then the probability of occurrence of the event is0

An unbiased die is thrown twice. Let the event A be 'odd number on the first throw' and B the event 'odd number on the second throw'. Check the independence of the events A and B.

If the probability of occurrence of an event is 5/8 then the odds in fovour of the event are-

A balanced coin is tossed three times in succession. Let A denote the event of getting 'head' in the first toss and B the event of getting 'tail' in the second toss. Prove that the events A and B are independent.

Two houses stand just on the opposite sides of a road of a village. A ladder that stands against the wall of the first house is at a distance of 6 metres from the house and makes an angle of 30^(@) with the horizontal line.But if the ladder stands against the wall of the second house keeping its foot at the same point, it makes an angle of 60^(@) with the horizontal line. (a) Find the length of the ladder. (b) Calculate the distance of the foot of the ladder from the foot of the wall of the second house. (c) Find the width of the road. Find the height where the top of the ladder is fixed against the wall of the second house.

The first trem of a GP is -3 and the square of the second term is equal to its 4th term. Find its 7th term.