Answer:
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)](https://img.qammunity.org/2021/formulas/mathematics/high-school/sknn59fncwfn01eak4zmsqhli5ozby29ot.png)
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)](https://img.qammunity.org/2021/formulas/mathematics/high-school/9fcrszgqmam3af5j6g3wl7yijo2mm3hi46.png)
Probability of getting diamond on second card =
![(12)/(51)](https://img.qammunity.org/2021/formulas/mathematics/college/22ywzv8kcxnl4j6l7th8qaq8mu9f7ftzkr.png)
Probability of getting diamond on both cards =
![(13)/(52) * (12)/(51)=(1)/(17)](https://img.qammunity.org/2021/formulas/mathematics/high-school/zz5qf1w71s5ofb41rda74el59impz91vlz.png)
So, The Probability of getting diamond on both cards is 1/17