Answer:
a. 11.26 % b. 6.76 %. It appears so since 6.76 % ≠ 15 %
Step-by-step explanation:
a. This is a binomial probability.
Let q = probability of giving out wrong number = 15 % = 0.15
p = probability of not giving out wrong number = 1 - q = 1 - 0.15 = 0.75
For a binomial probability, P(x) = ⁿCₓqˣpⁿ⁻ˣ. With n = 10 and x = 1, the probability of getting a number wrong P(x = 1) = ¹⁰C₁q¹p¹⁰⁻¹
= 10(0.15)(0.75)⁹
= 1.5(0.0751)
= 0.1126
= 11.26 %
b. At most one wrong is P(x ≤ 1) = P(0) + P(1)
= ¹⁰C₀q⁰p¹⁰⁻⁰ + ¹⁰C₁q¹p¹⁰⁻¹
= 1 × 1 × (0.75)¹⁰ + 10(0.15)(0.75)⁹
= 0.0563 + 0.01126
= 0.06756
= 6.756 %
≅ 6.76 %
Since the probability of at most one wrong number i got P(x ≤ 1) = 6.76 % ≠ 15 % the original probability of at most one are not equal, it thus appears that the original probability of 15 % is wrong.
24000 + 3000x = 30000 + 2400x
3000x - 2400x = 30,000 - 24,000
600x = 6000
x = 6000/600
x = 10 years
