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

A) 0.933

B) Not independent

Let us consider

'A' - made from natural polished wood

'B' - made from chrome accent

% of the boats are given. Thus the probability will be:

P(A) = 0.9

P(B) = 0.75  

P(AnB) = 0.7

1.) Probability of natural wood that it has chrome accent

The probability that if a boat has chrome accents it is also made of natural wood is 0.933.  

2.)  For an independent event :  

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

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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

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