what is the probability of not selecting a number 4 when a number cube is rolled if the probability of selecting a number 4 is 16?

Summary - The fundamental principle of counting (F.P.C) states that if an operation can be performed in m different ways and if for each such choice, another operation can be performed in n different ways, then both operations, in succession can be performed in exactly mn different ways. The princi..

If x be numerically so small that its cube and higher powers may be neglected, then find the binomial expansions for: i) (1 + 2x) - 4 ..

Some Applications of Binomial Theorem for Fractional Index - If x be numerically so small that its cube and higher powers may be x 3 , x 4 , x 5 , . are all approximately zero. If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (..

A histogram is a diagram which represents the class interval and the frequency in the form of a rectangle. There will be as many adjoining rectangles as there are class intervals. The class limits are marked on the horizontal axis. The frequency is marked on the vertical axis. Thus a rectang..

For the third term, take coefficient as n C 2 , power of 'a' as n-2 and power of 'b' as 2. Continue this process repeatedly till the last term n C n a 0 b n is obtained..

1. To find the sum of first n natural numbers. 2. To find the sum to squares of first n natural numbers. 3. To find the sum to the cubes of first n natural numbers. 4. Method of finding sum of a series whose nth term is know..

Let p(x) = x 4 +2x 3 -ax 2 +x-2 when p(x) is by x+2 [x- (-2)], R = p(-2) = (-2) 4 +2(-2) 3 -a(-2) 2 -2-2 = 16-16-4a-4 = -4a - 4 As (x+2) is a factor, R=0 -4a - 4 = 0 a = ..

The ratio a 2 : b 2 , obtained by compounding the ratio a : b with itself is called the duplicate ratio, . For example, the duplicate ratio of 4 : 9 is 4 2 : 9 2 = 16 : ..

i) (1 + 2x) - 4 ..

A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For example, x - y, a + 3b, x 3 + 4y etc. are binomials. We know that, For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical manner in terms of ..