For each element in a set of size 2n, an unbiased coin is tossed. All the 2n coin tossed are independent. An element is chosen if the corresponding coin toss were head. The probability that exactly n elements are chosen is
A. \[\frac{{\left( {\begin{array}{*{20}{c}} {2{\text{n}}} \\ {\text{n}} \end{array}} \right)}}{{{4^{\text{n}}}}}\]
B. \[\frac{{\left( {\begin{array}{*{20}{c}} {2{\text{n}}} \\ {\text{n}} \end{array}} \right)}}{{{2^{\text{n}}}}}\]
C. \[\frac{1}{{\left( {\begin{array}{*{20}{c}} {2{\text{n}}} \\ {\text{n}} \end{array}} \right)}}\]
D. $$\frac{1}{2}$$
Answer: Option A
This Question Belongs to Engineering Maths >> Probability And Statistics
A coin is tossed 4 times. What is the probability of getting heads exactly 3 times?
A. $$\frac{1}{4}$$
B. $$\frac{3}{8}$$
C. $$\frac{1}{2}$$
D. $$\frac{3}{4}$$
A. 1 and $$\frac{1}{3}$$
B. $$\frac{1}{3}$$ and 1
C. 1 and $$\frac{4}{3}$$
D. $$\frac{1}{3}$$ and $$\frac{4}{3}$$
A. E(XY) = E(X) E(Y)
B. Cov (X, Y) = 0
C. Var (X + Y) = Var (X) + Var (Y)
D. E(X2Y2) = (E(X))2 (E(Y))2
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