Answer: [tex]\dfrac{15}{17}[/tex]
Step-by-step explanation:
Total number of cards in a deck = 52
Number of red cards = 26
Number of cards not red =
Number of ways to draw not red cards = [tex]^{26}C_3[/tex]
Total ways to draw 3 cards = [tex]^{52}C_3[/tex]
The probability that none of three cards are red = [tex]\dfrac{^{26}C_3}{^{52}C_3}[/tex]
[tex]=\dfrac{\dfrac{26!}{3!(26-3)!}}{\dfrac{52!}{3!(52-3)!}}[/tex] [∵ [tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]]
[tex]=\dfrac{\dfrac{26\times25\times24\times23!}{(23)!}}{\dfrac{52\times51\times50\times49!}{3!(49)!}}=\dfrac{2}{17}[/tex]
Now , the probability that at least one of the cards drawn is a red card = 1- Probability that none cards are red
[tex]=1-\dfrac{2}{17}=\dfrac{17-2}{17}=\dfrac{15}{17}[/tex]
Hence, the required probability = [tex]\dfrac{15}{17}[/tex]
