Question

you are craving mrs field's cookies. you have a choice of oatmeal raisin, macadamia nut, triple chocolate, cinamon sugar, chocolate chip, and peanut butter. if you must choose at least one cookie:
what is the probability that you do not take cookies that contain chocolate?

Answer 1

Number of cookies = 6

Number of cookies with chocolate = 2

Number of cookies without chocolate = 4

P(you do not take cookies that contain chocolate) = Number of cookies without chocolate / Total number of cookies

= 4/6

= 2/3

If two cookies are taken, P(not containing chocolate cookie) = 4C2/6C2 [nCr = n!/(r! x (n-r)!]

= 6/15

= 2/5

If three cookies are taken, P(not containing chocolate cookie) = 4C3/6C3

= 4/20

= 1/5

If 4 cookies are taken, P(not containing chocolate cookie) = 4C4/6C4

= 1/15

If 5 cookies are taken, P(not containing chocolate cookie) = 0

If 6 cookies are taken, P(not containing chocolate cookie) = 0

Assuming that you are equally likely to select 1, 2, 3, 4, 5 or 6 cookies, that is each scenario has a probability of 1/6

P(you do not take cookies that contain chocolate) = 1/6 (2/3 + 2/5 + 1/5 + 1/15 + 0 + 0)

= 2/9