Answer to Question #183169 in Statistics and Probability for KLAUSXMİKE

Question

Suppose that the discrete random variable X counts the number of heads in four tosses of a balanced coin. What is the probability of tossing at least two heads?

Answer 1

p = probability of head in a toss

p = 0.5

X~Binomial(4,0.5)

$P(X≥2) = 1 -P(X<2) \\ = 1 -(P(X=0) + P(X=1)) \\ = 1 -(C^4_0(0.5)^0(0.5)^4 + C^4_1(0.5)^1(0.5)^3) \\ = 1 -(0.5^4 + 4(0.5)^4) \\ = 1 -0.5^4(1+4) \\ = 1 -0.3125 \\ = 0.6875$