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A card is drown from each of two well-shuffled packs of cards.The probability that at least one of them is an ace is
  • a)
    1
  • b)
    25
  • c)
    2
  • d)
    none 169 169 13
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A card is drown from each of two well-shuffled packs of cards.The prob...
**Solution:**

To find the probability that at least one of the cards drawn is an ace, we can use the concept of complementary probability.

**Complementary Probability:**
The complementary probability of an event A is the probability that event A does not occur. Mathematically, it can be represented as P(A') = 1 - P(A).

In this case, let's consider the event A as the event that none of the cards drawn is an ace. We need to find the complementary probability P(A') which represents the probability that at least one of the cards drawn is an ace.

**Step 1: Calculate the probability of not drawing an ace:**
In a standard deck of cards, there are 52 cards with 4 aces. Therefore, the probability of not drawing an ace from a single deck is given by:
P(not drawing an ace) = (number of cards that are not aces) / (total number of cards)
= (52 - 4) / 52
= 48 / 52
= 12 / 13

**Step 2: Calculate the probability of not drawing an ace from both decks:**
Since we have two well-shuffled packs of cards, the probability of not drawing an ace from both packs is the product of the probabilities of not drawing an ace from each pack. Therefore,
P(not drawing an ace from both packs) = (12/13) * (12/13)
= 144/169

**Step 3: Calculate the complementary probability:**
Finally, we can find the probability that at least one of the cards drawn is an ace by subtracting the probability of not drawing an ace from both packs from 1.
P(at least one ace) = 1 - P(not drawing an ace from both packs)
= 1 - (144/169)
= 169/169 - 144/169
= 25/169

Therefore, the correct answer is option B) 25/169.
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A card is drown from each of two well-shuffled packs of cards.The probability that at least one of them is an ace isa)1b)25c)2d)none 169 169 13Correct answer is option 'B'. Can you explain this answer?
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