For the next three (03) items that follow : Let A, B, C and D be mutually exclusive and exhaustive events such that \(\dfrac{P(A)}{6} = \dfrac{P(B)}{3} = \dfrac{P(C)}{4} = \dfrac{P(D)}{2}\).
If H is the harmonic mean of P(A), P(B), P(C) and P(D), then what is H equal to?
\(\dfrac{16}{75}\)
Using \(P(A)=\dfrac{2}{5}, P(B)=\dfrac{1}{5}, P(C)=\dfrac{4}{15}, P(D)=\dfrac{2}{15}\), the harmonic mean is \(H=\dfrac{4}{\frac{1}{P(A)}+\frac{1}{P(B)}+\frac{1}{P(C)}+\frac{1}{P(D)}} = \dfrac{4}{2.5+5+3.75+7.5} = \dfrac{4}{18.75} = \dfrac{16}{75}\).
Similar Questions
Let x be the HM and y be the GM of two positive numbers m and n. If 5x = 4y, then which one of the following is correct?
Consider the following statements:
1. cos θ + sec θ can never be equal to 1.5.
2. tan θ + cot θ can never be less than 2.
Which of the above statements is/are correct?If \({{\rm{x}}^{{\rm{In}}\left( {\frac{{\rm{y}}}{{\rm{z}}}} \right)}} \cdot {{\rm{y}}^{{\rm{In}}{{\left( {{\rm{xz}}} \right)}^2}}} \cdot {{\rm{z}}^{{\rm{In}}\left( {\frac{{\rm{x}}}{{\rm{y}}}} \right)}} = {{\rm{y}}^{4{\rm{\;In\;y}}}}\) for any x > 1, y > 1 and z > 1, then which one of the following is correct?
Consider the following measures of central tendency for a set of N numbers:
1. Arithmetic mean.
2. Geometric mean.
Which of the above uses/use all the data?
If G is the geometric mean of P(A), P(B), P(C) and P(D), then what is G equal to?
What is the minimum value of a 2x + b 2y where xy = c 2?
Important Questions from Relations between AM, GM, HM
If p = tan2 x + cot2 x, then which one of the following is correct?
If \(a_1, a_2, a_3,...,a_n\) are positive real numbers whose product is a fixed number C, then the minimum value of \(a_1+a_2+...+a_n\) is
In an acute angled ΔABC, the least value of sec A + sec B + sec C is:
Let x be the HM and y be the GM of two positive numbers m and n. If 5x = 4y, then which one of the following is correct?
Consider the following statements:
1. cos θ + sec θ can never be equal to 1.5.
2. tan θ + cot θ can never be less than 2.
Which of the above statements is/are correct?
