Given:
Two cards are selected from a standard deck of 52 playing cards.
The first card is not replaced before the second card is selected.
To find:
The probability of selecting a four and then selecting a two.
Solution:
We know that,
Total number of cards = 52
Number of four cards = 4
Number of two cards = 4
Now,
[tex]\text{Probability}=\dfrac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}[/tex]
Probability of selecting a four = [tex]\dfrac{4}{52}[/tex]
After selecting a card, then number of remaining cards is 51.
Probability of selecting a two = [tex]\dfrac{4}{51}[/tex]
So, the probability of selecting a four and then selecting a two is
[tex]P=\dfrac{4}{52}\times \dfrac{4}{51}[/tex]
[tex]P=\dfrac{1}{13}\times \dfrac{4}{51}[/tex]
[tex]P=\dfrac{4}{663}[/tex]
Therefore, the required probability is [tex]\dfrac{4}{663}[/tex].
