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A bag contains 40 u.s. quarters and 10 canadian quarters. (the coins are identical in size.) if 7 quarters are picked from the bag, what is the probability of getting at least one canadian quarter? (round your answer to one decimal place. ___ %

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Answer:

Explanation:

To calculate the probability of getting at least one Canadian quarter when picking 7 quarters from the bag, you can use the complementary probability approach. The complementary probability is the probability of the event not happening (in this case, not getting any Canadian quarters) and subtracting it from 1.

First, let's find the probability of not getting any Canadian quarters in 7 draws.

The probability of drawing a U.S. quarter on each draw is (40 U.S. quarters) / (total quarters) = 40 / (40 + 10) = 4/5.

Now, the probability of not getting a Canadian quarter in one draw is the complementary probability, which is 1 - (probability of getting a U.S. quarter) = 1 - (4/5) = 1/5.

Since each draw is independent, you can multiply the probabilities for each draw to find the probability of not getting a Canadian quarter in all 7 draws:

(1/5) * (1/5) * (1/5) * (1/5) * (1/5) * (1/5) * (1/5) = (1/5)^7

Now, we can calculate the complementary probability of getting at least one Canadian quarter:

1 - (1/5)^7 ≈ 0.99994

To express this probability as a percentage, multiply by 100:

0.99994 * 100 ≈ 99.99%

So, the probability of getting at least one Canadian quarter when picking 7 quarters from the bag is approximately 99.99%, rounded to one decimal place.

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