ProbabilityHardBloom L3
Question
If ' $n$ ' different things are distributed among $x$ boys and $y$ girls. Find the probability that the number of things received by girls is even.
Options
A.$1 - \left( \frac{x - y}{x + y} \right)^{n}$
B.$\frac{1}{2} - \frac{1}{2}\left( \frac{x - y}{x + y} \right)^{n}$
C.$1 - \frac{1}{2}\left( \frac{x - y}{x + y} \right)^{n}$
D.$\frac{1}{2} + \frac{1}{2}\left( \frac{x - y}{x + y} \right)^{n}$
Solution
Sol. [Key Concept: Distribute $n$ things to $x$ boys; the even-power binomial sum applies.]
$$\begin{matrix} P & \ = \frac{\ ^{n}C_{0}x^{n}y^{\circ} + \ ^{n}C_{2}x^{n - 2}y^{2} + \ ^{n}C_{4}x^{n - 4}y^{4} + \ldots.}{(x + y)^{n}} \\ & \ = \frac{(x + y)^{n} + (x - y)^{n}}{2(x + y)^{n}} \end{matrix}$$
Create a free account to view solution
View Solution FreeMore Probability Questions
Two dice are thrown together. The probability that the sum of their numbers be at least 5 is-...A bag A contains 2 white and 3 red balls and bag B contains 4 white and 5 red balls. One ball is drawn at random from a ...From $(4\text{ }m + 1)$ tickets numbered as $1,2,3,\ldots.,4\text{ }m + 1$; three tickets are chosen at random. Then the...Three dice are thrown simultaneously. What is the probability of obtaining a total of 17 or 18-...From a pack of 52 playing cards. face cards and tens are removed and kept aside then a card is drawn at random from the ...