You have 10 candies in your pocket, 3 apple flavored, 5 grape flavored, and 2 watermelon flavored. Now you randomly take a candy from your pocket and put it in your mouth, so what is the probability that the candy is apple-flavored? (Please express in percentage terms)At this point your friend comes over, so you take two candies from your pocket and hand it to your friend. So what is the probability that both candies are grape-flavored? (Retain four decimal places) (don't use %)
Question
You have 10 candies in your pocket, 3 apple flavored, 5 grape flavored, and 2 watermelon flavored. Now you randomly take a candy from your pocket and put it in your mouth, so what is the probability that the candy is apple-flavored? (Please express in percentage terms)At this point your friend comes over, so you take two candies from your pocket and hand it to your friend. So what is the probability that both candies are grape-flavored? (Retain four decimal places) (don't use %)
Solution
- The probability that the candy is apple-flavored:
There are 3 apple-flavored candies and 10 candies in total. So, the probability that the candy is apple-flavored is 3/10 = 0.3 or 30%.
- The probability that both candies are grape-flavored:
After you take one candy for yourself, there are 9 candies left in your pocket. You then take two candies for your friend.
The probability that the first candy is grape-flavored is 5/9.
After taking one grape-flavored candy, there are 4 grape-flavored candies left and 8 candies in total. So, the probability that the second candy is also grape-flavored is 4/8 = 0.5.
Since these are independent events, the probability that both candies are grape-flavored is the product of the individual probabilities:
(5/9) * (4/8) = 0.2778 (rounded to four decimal places).
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