Question

A standard deck of 52 cards contains 4 suits: hearts, dimadons, clubs n spades. Each suit has 13 cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack ,queen, and king. 2 cards r randomly drawn without replacement. Calculate da probability of drawing 2 dimnds card express ur answer in percent from rounding 2 da nearest hundredth

Answer 1

To find the probability of drawing 2 diamonds from a standard deck of 52 cards without replacement, we can use the following steps:

1. Determine the number of diamonds in the deck: There are 13 diamond cards in total.

2. Find the probability of the first draw:

   • The probability of drawing a diamond on the first draw is: \[ P(\text{First diamond}) = \frac{13}{52} = \frac{1}{4} \]

3. Find the probability of the second draw:

   • After drawing one diamond, there are now 12 diamonds left in a deck of 51 cards. So the probability of drawing another diamond is: \[ P(\text{Second diamond | First diamond}) = \frac{12}{51} \]

4. Calculate the overall probability of drawing 2 diamonds: \[ P(\text{2 diamonds}) = P(\text{First diamond}) \times P(\text{Second diamond | First diamond}) = \frac{13}{52} \times \frac{12}{51} \] Simplifying this: \[ P(\text{2 diamonds}) = \frac{13 \times 12}{52 \times 51} = \frac{156}{2652} \]

5. Simplify the fraction: \[ \frac{156}{2652} = \frac{1}{17} \quad (\text{dividing numerator and denominator by 156}) \]

6. Convert to decimal and then to percentage: \[ P(\text{2 diamonds}) \approx 0.0588235294 \] To convert this to percentage: \[ 0.0588235294 \times 100 \approx 5.88235294% \]

7. Round to the nearest hundredth: \[ P(\text{2 diamonds}) \approx 5.88% \]

Therefore, the probability of drawing 2 diamond cards from a standard deck, expressed as a percentage rounded to the nearest hundredth, is 5.88%.