A deck of special cards has the following distribution shown in the frequency table.
If a card is drawn randomly and not replaced, and then a second card is drawn, what is the probability that the first card is a heart and the second card is a moon?
Options
A
B
C
D
Answer & Analysis
Answer
C
Analysis
Question Analysis
This question involves calculating the probability of two events occurring in sequence using a frequency table.
The main focus is on recognizing that since the card is not replaced after the first draw, these are dependent events, and applying the multiplication rule for dependent events to find the combined probability.
Key Concept Explanation
Dependent events are those where the outcome of one event affects the outcome of the other.
For two dependent events and , the probability of both and occurring is given by , where is the probability of event occurring given that event has already occurred.
The probability of an individual event is calculated as , and the probability of the second event needs to be adjusted based on the change in the total number of items after the first event occurs.
Step-by-Step Solution
First, find the total number of cards:
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