What is the probability of drawing 2 cards in succession (without replacement) from a standard deck of playing cards and having them both be hearts?

Question
Probability
asked 2021-03-02
What is the probability of drawing 2 cards in succession (without replacement) from a standard deck of playing cards and having them both be hearts?

Answers (1)

2021-03-03
The outcome of the first draw affects the next draw so the events are dependent. So, we have:
P(heart and heart)=P(heart)*P(heart then heart)
The probaability that a heart card is draw on the first draw is: P(heart)=\(\displaystyle\frac{{13}}{{52}}=\frac{{1}}{{4}}\)
The probaability that a heart card is draw on the second draw is: P(heart)=\(\displaystyle\frac{{12}}{{51}}=\frac{{4}}{{17}}\)
So. the probaability of drawing 2 hearts in succession without replacement is: P(heart and heart)=\(\displaystyle\frac{{1}}{{4}}\cdot\frac{{4}}{{17}}\) P(heart and heart)=\(\displaystyle\frac{{1}}{{17}}\)
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