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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

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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

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

[tex]P(\frac{A}{B}) = \frac{P(AnB)}{P(B)}\\\\P(\frac{A}{B}) =\frac{0.7}{0.75}\\\\P(\frac{A}{B}) =0.933[/tex]

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

2.)  For an independent event :  

[tex]P(A\text{ n}B) = P(A) * P(B)\\\\P(A\text{ n}B)= 0.9 * 0.75\\\\P(A\text{ n}B) = 0.675[/tex]

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

Learn more:

brainly.com/question/12594357

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