Question

At an antique boat show, 90% of the boats are made of a natural, polished wood. 75% of the boats have some chrome accents on the boat on at least one visible feature. And 70% have both features.
A) What is the probability that if a boat has chrome accents it is also made of natural wood?
B) Are having chrome accents and being made of wood independent characteristics? Explain using probabilities

Answer 1

Answer:

0.933 ; not independent

Step-by-step explanation:

Given :

A - made from natural polished wood

B - made from chrome accent

P(A) = 0.9

P(B) = 0.75

P(AnB) = 0.7

1.) probability of natural wood Giveb that it has chrome accent

P(A|B) = P(AnB) / P(B)

P(A|B) = 0.7 / 0.75

P(A|B) = 0.933

2.)

For an independent event :

P(AnB) = p(A) * p(B)

P(AnB) = 0.9 * 0.75 = 0.675

However, p(AnB) Given here is 0.7, thus the event aren't independent