Multiple choice

A pack of cards consists of $15$ cards numbered $1$ to $15$. Three cards are drawn at random with replacement. Then, the probability of getting two odd and one even numbered cards, is?

  1. $\dfrac{348}{1125}$
  2. $\dfrac{398}{1125}$
  3. $\dfrac{448}{1125}$
  4. $\dfrac{498}{1125}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Odd numbers are {1, 3, 5, 7, 9, 11, 13, 15} (8 cards). Even numbers are {2, 4, 6, 8, 10, 12, 14} (7 cards). P(Odd) = 8/15, P(Even) = 7/15. We need 2 odd and 1 even in 3 draws. This is a binomial scenario: 3C2 * (8/15)^2 * (7/15)^1 = 3 * (64/225) * (7/15) = 1344 / 3375. Dividing by 3 gives 448 / 1125.

AI explanation

Out of 15 cards numbered 1 to 15, there are 8 odd numbered cards and 7 even numbered cards. The probability of drawing an odd card is 8/15 and an even card is 7/15. Using the binomial probability formula for 2 odd and 1 even card out of 3 draws, we calculate 3C2 multiplied by (8/15)^2 multiplied by (7/15). This yields 3 times 64/225 times 7/15, which simplifies to 1344 divided by 3375, or 448/1125.

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