Question

1. In a random sample of male and female New York street performers between the ages of 22-35 you know that:

The probability a man is a mime is 0.30.

the probability a woman is a spray paint artist is 0.165

The probability a man is a break dancer; given that he’s a mime is 0.250.

The probability a woman is a faux statue is 0.550.

The probability a woman is a faux statue, given that she’s a spray paint artist is .065.

Compute the following probabilities: (6 points: 2 points for each problem)

a.P(woman is a spray paint artist and a faux statue)

b.P (woman is a spray paint artist or a faux statue)



c.P (man is a mime and a break dancer)

Answer 1

P(man is a mine) = 0.3

P(woman is a spray paint artist) = 0.165

P(man is break dancer | he's a mine) = 0.25

P(woman is a faux statue) = 0.55

P(woman is a faux statue | she’s a spray paint artist) = 0.065

a) P(woman is a spray paint artist and a faux statue) = P(woman is a faux statue | she’s a spray paint artist) * P(woman is a spray paint artist)

                                                     = 0.065 * 0.165

                                                     = 0.011

b) P(woman is a spray paint artist or a faux statue) = P(woman is a spray paint artist) + P(woman is a faux statue) - P(woman is a spray paint artist and a faux statue)

                                                                                  = 0.165 + 0.55 - 0.011

                                                                                  = 0.704

c) P(man is a mime and a break dancer) = P(man is break dancer | he's a mine) * P(man is a mine)

                                                                 = 0.25 * 0.3

                                                                 = 0.075