Probability that all the three cards are of king without replacing a card is equals to [tex]\frac{1}{5525}[/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,
Total number of cards = 52
Condition given to choose a card is without replacing
Total number of king cards = 4
Probability of choosing first king card 'P(A) ' = [tex]\frac{4}{52}[/tex]
Probability of choosing second king card ' P(B)' = [tex]\frac{3}{52}[/tex]
Probability of choosing third king card 'P(C)'= [tex]\frac{2}{52}[/tex]
Probability that all the three cards are of king without replacing a card
= P(A) × P(B) × P(C)
= [tex]\frac{4}{52}[/tex] ×[tex]\frac{3}{52}[/tex] ×[tex]\frac{2}{52}[/tex]
= [tex]\frac{1}{5525}[/tex]
Hence, probability that all the three cards are of king without replacing a card is equals to [tex]\frac{1}{5525}[/tex].
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