Question

Kurt was a spectator at his town's air guitar competition. Contestants were allowed to play either the acoustic or electric air guitar, but not both. Kurt recorded which type of guitar each contestant played. He also counted the number of contestants wearing different kinds of pants, as there were some interesting stylistic choices. Acoustic guitar Electric guitar Leather 2 5 Velvet 7 9 Sequins 11 3 What is the probability that a randomly selected contestant was dressed in velvet or played an acoustic guitar? Simplify any fractions.

Answer 1

Probability that he is dressed in Velvet =

`\frac{7\text{ + 9}}{2\text{ + 5 + 7 + 9 + 11 + 3 }}\text{ = }(16)/(37)`

Probability that he is dressed in Acoustic Guitar =

`\frac{2\text{ + 7 + 11}}{2\text{ + 5 + 7 + 9 + 11 + 3 }}\text{ = }(20)/(37)`

Recall that P ( V n A ) =

`\frac{7}{2\text{ + 5 + }7\text{ + 9 + 11 + 3}}\text{ = }(7)/(37)`

Finally, we have to calculate : P ( V or A ) = P ( V ) + P ( A ) - P ( V n A )

( because they are not mutually - exclusive )

`\frac{16}{37\text{ }}\text{ + }(20)/(37)\text{ - }\frac{7}{37\text{ }}\text{ = }(29)/(37)`

CONCLUSION: The final answer is:

`(29)/(37)`