A container holds 15 small figurines, 6 are animals, 5 are superheroes, and 4 are cartoon characters. Two figurines are drawn one after another without replacement. The probability that the first figurine is a superhero and the second figurine is a cartoon character is ____.
Answer & Analysis
Analysis
Question Analysis
This question is about calculating the probability of two consecutive dependent events.
The core task is to precisely determine the probabilities of each draw as the composition of figurines in the container changes after the first draw, and correctly apply the multiplication rule for dependent events to obtain the combined probability of both events.
Key Concept Explanation
Dependent events mean that the result of the first draw impacts the probability of the second draw.
In this non - replacement scenario, when the first figurine is taken out, the total number of figurines and the number of figurines in each category decrease, which in turn modifies the probabilities for the second draw.
Step-by-Step Solution
Calculate the probability of drawing a superhero figurine on the first draw:
There are 5 superhero figurines out of 15 total figurines. So, .
Calculate the probability of drawing a cartoon character figurine on the second draw given that a superhero figurine was drawn on the first draw:
After removing one superhero figurine, there are 14 figurines left, and 4 of them are cartoon characters. So,
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