Question

In a bag of sweets, 6 are orange and 9 are lime. Jodi chooses a sweet at random, eats it an

then chooses a second sweet at random.
What is the probability that both sweets are the same flavour?
(3 Points)
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Answer 1

Answer:
`(17)/(35)`

Explanation:

Given

The bag contains 6 orange and 9 lime sweets

For both sweets of the same flavor, Jodi must either choose orange or lime

No. of ways it can be done is
`^6C_1*^5C_1+^9C_1*^8C_1`

The total no of ways of selecting two sweets out of 15 is
`^(15)C_1*^(14)C_1`

The probability that both sweets are the same flavor

`P=(^6C_1*^5C_1+^9C_1*^8C_1)/(^(15)C_1*^(14)C_1)=(102)/(210)=(51)/(105)=(17)/(35)`