Question

Based on a Harris Interactive poll, 20% of adults believe in reincarnation. Assume that 6 adults are randomly selected.

Determine each probability to 4 decimal places.

A. Exactly 5 of the selected adults believe in reincarnation

B. At least 5 of the randomly selected adults believe in reincarnation

C. At most 5 of the randomly selected adults believe in reincarnation

Answer 1

Given that ,

p = 0.20

1 - p = 1 - 0.20= 0.80

(a)n =6

Using binomial probability formula ,

P(X = x) = (_n C _x) * p^x * (1 - p)^{n - x}

P(X = 5) = (₆ C ₅) * (0.20)⁵ * (0.80)¹

^=0.0015

^{probability=0.0015}

(b)Using binomial probability formula ,

P(X = x) = (_n C _x) * p ^x * (1 - p)^{n - x}

P(X >5 ) = 1 - P( x <5)

= 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3) - P(X = 4) - P(X = 5)

= 1 -  (₆ C 0) * (0.20)⁰ * (0.80)⁶ -  (₆ C ₁) * (0.20)¹ * (0.80)⁵ -  (₆  C ₂) * (0.20)² * (0.80)⁴ -  (₆  C ₃) * (0.20)³ * (0.80)³ -  (₆ C ₄) * (0.20)⁴ * (0.80)² -  (₆ C ₅) * (0.20)⁵ * (0.80)¹

=0.0016

^{probability=0.0016}

(c)P(X < 5) = P(X = 0) +P(X = 1) +P(X = 2) +P(X = 3) +P(X = 4) +P(X = 5)

=(₆ C 0) * (0.20)⁰ * (0.80)⁶ + (₆ C ₁) * (0.20)¹ * (0.80)⁵ + (₆  C ₂) * (0.20)² * (0.80)⁴ + (₆  C ₃) * (0.20)³ * (0.80)³ + (₆ C ₄) * (0.20)⁴ * (0.80)² + (₆ C ₅) * (0.20)⁵ * (0.80)¹

Probability = 0.9999