Respuesta :
The probability that a pair is not drawn = 0.765
Step-by-step explanation:
Here, the total number of cards in the given deck = 52
The total number of suits = 4 (13 cards each)
Now, P( Drawing 2 clubs) = [tex]\frac{^{13}C_2}{^{52}C_2} = \frac{78}{1326} = (\frac{1}{17} )[/tex]
Similarly, P( Drawing 2 diamond ) = [tex]\frac{^{13}C_2}{^{52}C_2} = \frac{78}{1326} = (\frac{1}{17} )[/tex]
P( Drawing 2 spades) = [tex]\frac{^{13}C_2}{^{52}C_2} = \frac{78}{1326} = (\frac{1}{17} )[/tex]
P( Drawing 2 hearts ) = [tex]\frac{^{13}C_2}{^{52}C_2} = \frac{78}{1326} = (\frac{1}{17} )[/tex]
⇒ Probability of drawing 2 clubs or 2 spades or 2 hearts or 2 diamonds
= P( Drawing 2 clubs) + P( Drawing 2 diamond ) P( Drawing 2 spades)+ P( Drawing 2 hearts ) = [tex](\frac{1}{17})+ (\frac{1}{17})+ (\frac{1}{17})+ (\frac{1}{17}) = 4\times (\frac{1}{17}) = \frac{4}{17} = 0.2352[/tex]
Now, P(NOT DRAWING A PAIR) = 1 - P(DRAWING a PAIR)
= 1- 0.2352 = 0.7647
Hence, the probability that a pair is not drawn = 0.7647
