Question

The Magazine Mass Marketing Company has received 1010 entries in its latest sweepstakes. They know that the probability of receiving a magazine subscription order with an entry form is 0.60.6. What is the probability that more than a fifth of the entry forms will include an order?

Answer 1

X ~ bin ( n , p)

Where n = 10 , p = 0.6

Binomial probability distribution is

P(X) = ⁿC_x * p^x * ( 1 - p)^n-x

P(X > 5) = P(X >= 6)

= P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9) + P(X = 10)

= ¹⁰C₆ * 0.6⁶ * ( 1 - 0.6)⁴ + ¹⁰C₇ * 0.6⁷ * ( 1 - 0.6)³ + ¹⁰C₈ * 0.6⁸ * ( 1 - 0.6)² + ¹⁰C₉ * 0.6⁹ * ( 1 - 0.6) +

¹⁰C₁₀ * 0.6¹⁰ * ( 1 - 0.6)⁰

= 0.6331