A bag has 15 candies, 5 strawberry - flavored, 6 chocolate - flavored, and 4 lemon - flavored. Four candies are drawn without replacement. The probability that the first candy is strawberry - flavored, the second is chocolate - flavored, the third is lemon - flavored, and the fourth is strawberry - flavored again is ____.
Answer & Analysis
Analysis
Question Analysis
This question is centered around calculating the probability of four successive dependent events.
The main emphasis is on accurately determining the probabilities of each draw as the composition of candies in the bag changes with each draw and correctly applying the multiplication rule for multiple dependent events to find the combined probability of the four events.
Key Concept Explanation
Dependent events imply that the outcome of each previous candy draw affects the probabilities of the subsequent draws.
As a candy is taken out, the total number of candies and the number of candies of each flavor in the bag change, which impacts the likelihood of drawing a candy of a particular flavor in the next draw.
Step-by-Step Solution
Calculate the probability of drawing a strawberry - flavored candy on the first draw:
There are 5 strawberry - flavored candies out of 15 total candies, so .
After removing one strawberry - flavored candy, there are 14 candies left, and 6 of them are chocolate - flavored. So .
After removing a strawberry - flavored and a chocolate - flavored candy, there are 13 candies left, and 4 of them are lemon - flavored. So .
After...
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