Probability of getting an Ace, 2, and 3, at random from a deck without replacement is equals to [tex]\frac{8}{16,575}[/tex].
" Probability is defined as the ratio of number of favourable outcomes to the total number of outcomes."
Formula used
Probability = [tex]\frac{Number of favourable outcomes}{Total number of outcomes}[/tex]
According to the question,
Number of cards to choose = 3
Total number of cards = 52
Number of Ace cards =4
Number of 2 cards = 4
Number of 3 cards = 4
Condition of without replacement,
Probability of getting as first card P(A) = [tex]\frac{4}{52}[/tex]
Probability of getting second card P(B)= [tex]\frac{4}{51}[/tex]
Probability of getting second card P(C) = [tex]\frac{4}{50}[/tex]
Probability of getting an Ace, 2, and 3, without replacement
= P(A)× P(B)× P(C)
= [tex]\frac{4}{52}[/tex] × [tex]\frac{4}{51}[/tex]×[tex]\frac{4}{50}[/tex]
= [tex]\frac{8}{16,575}[/tex]
Hence, probability of getting an Ace, 2, and 3, at random from a deck without replacement is equals to [tex]\frac{8}{16,575}[/tex].
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