Four fair coins are tossed once. Calculate the probabilit...
Four fair coins are tossed once. Calculate the probability of having equal heads and tails.
\(\frac{1}{4}\)
\(\frac{3}{8}\)
\(\frac{1}{2}\)
\(\frac{15}{16}\)
Correct answer is B
Let \(p(head) = p = \frac{1}{2}\) and \(p(tail) = q = \frac{1}{2}\)
\((p + q)^{4} = p^{4} + 4p^{3}q + 6p^{2}q^{2} + 4pq^{3} + q^{4}\)
The probability of equal heads and tails = \(6p^{2}q^{2} = 6(\frac{1}{2}^{2})(\frac{1}{2}^{2})\)
= \(\frac{6}{16} = \frac{3}{8}\).
Given that \(y = x(x + 1)^{2}\), calculate the maximum value of y....
The position vectors of A and B are (2i + j) and (-i + 4j) respectively; find |AB|. ...
There are 7 boys in a class of 20. Find the number of ways of selecting 3 girls and 2 boys ...
>Evaluate: \(\int(2x + 1)^3 dx\)...
Given that \(\tan x = \frac{5}{12}\), and \(\tan y = \frac{3}{4}\), Find \(\tan (x + y)\)....
Find the magnitude and direction of the vector \(p = (5i - 12j)\)...
Find the constant term in the binomial expansion \((2x^{2} + \frac{1}{x})^{9}\)...