Question

fill in the blank 20 points
ms. mathy surveyed 430 men and 200 women about their vehicles. of those surveyed, 160 men and 85 women said they own a blue vehicle. complete the table and then answer each question. write all answers as fractions in simplest form.

	blue	not blue
women	type your answer	type your answer

a) if a randomly chosen person is a woman, what is the probability of that person having car that is not blue? type your answer...

b) ( p(\text{blue}) = ) type your answer...

c) ( p(\text{men} mid \text{not blue}) = ) type your answer...

d) ( p(\text{women} cap \text{blue}) = ) type your answer...

Explanation:

Step1: Complete the table

• Men: Blue = 160, Not Blue = 430 - 160 = 270
• Women: Blue = 85, Not Blue = 200 - 85 = 115

So the table is:

	Blue	Not Blue
Women	85	115

Step2: Solve Part A

• Total women = 200, Women with not blue = 115
• Probability = $\frac{115}{200} = \frac{23}{40}$

Step3: Solve Part B

• Total surveyed = 430 + 200 = 630
• Total Blue = 160 + 85 = 245
• Total Not Blue = 630 - 245 = 385
• $P(\text{Blue})' = \frac{385}{630} = \frac{11}{18}$ (simplified by dividing numerator and denominator by 35)

Step4: Solve Part C

• $P(\text{Men} | \text{Not Blue}) = \frac{\text{Men and Not Blue}}{\text{Total Not Blue}} = \frac{270}{385} = \frac{54}{77}$ (simplified by dividing numerator and denominator by 5)

Step5: Solve Part D

• $P(\text{Women} \cap \text{Blue}) = \frac{\text{Women and Blue}}{\text{Total surveyed}} = \frac{85}{630} = \frac{17}{126}$ (simplified by dividing numerator and denominator by 5)

Answer:

A) $\frac{23}{40}$
B) $\frac{11}{18}$
C) $\frac{54}{77}$
D) $\frac{17}{126}$
Table:

	Blue	Not Blue
Women	85	115