Multiple choice

Four coins are tossed together. What is the probability that head will appear on at least one of the four?

  1. $\displaystyle\frac{15}{16}$
  2. $\displaystyle\frac{1}{16}$
  3. $\displaystyle\frac{1}{4}$

  4. None of these
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A Correct answer
Explanation

The probability of at least one head is 1 minus the probability of no heads. The probability of getting no heads (all tails) in 4 tosses is (1/2)^4 = 1/16. Thus, 1 - 1/16 = 15/16.

AI explanation

The total number of possible outcomes when tossing four coins is 2^4, which equals 16. Instead of calculating the probability of getting at least one head directly, it is simpler to use the complementary event method by finding the probability of getting no heads at all. The probability of getting all tails is 1 / 16, so subtracting this from 1 gives the probability of at least one head as 1 - 1/16 = 15/16.

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