Question

Find the probability.

6) A cooler contains twelve bottles of sportsdrink: three lemon-lime flavored, fourorange flavored, and five fruit-punchflavored. You randomly grab a bottle. Then you return the bottle to the cooler,mix up the bottles, and randomly selectanother bottle. Both times you get alemon-lime drink.

7) You select two cards from a standardshuffled deck of 52 cards. Both selectedcards are diamonds. (Note that 13 of the 52cards are diamonds.)

Answer 1

The Probability of getting lemon drink on both draws is 1/16

The Probability of getting diamond on both cards is 1/17

Explanation:

1)

No. of lemon-lime flavored bottle = 3

No. of orange flavored bottle = 4

No. of fruit punch flavored bottle = 5

Total bottles = 12

We are given that You randomly grab a bottle. Then you return the bottle to the cooler,mix up the bottles, and randomly select another bottle. Both times you get a lemon-lime drink.

Probability of getting lemon drink on both draws with replacement =
`(3)/(12) * (3)/(12) = (1)/(16)`

So, The Probability of getting lemon drink on both draws is 1/16

2)

No. of diamond cards = 13

Total cards =52

Probability of getting diamond on first card =
`(13)/(52)`

Probability of getting diamond on second card =
`(12)/(51)`

Probability of getting diamond on both cards =
`(13)/(52) * (12)/(51)=(1)/(17)`

So, The Probability of getting diamond on both cards is 1/17