Multiple choice

The probability is $\displaystyle \frac { 1 }{ 2 } $ that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

  1. $\displaystyle \frac { 1 }{ 8 } $
  2. $\displaystyle \frac { 1 }{ 2 } $
  3. $\displaystyle \frac { 3 }{ 4 } $
  4. $\displaystyle \frac { 7 }{ 8 } $
  5. $\displaystyle \frac { 15 }{ 16 } $
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D Correct answer
Explanation

The probability of at least one tail is 1 minus the probability of getting no tails (all heads). The probability of all heads in 3 tosses is (1/2)^3 = 1/8. Thus, 1 - 1/8 = 7/8.

AI explanation

The probability of getting at least one tail in three tosses is found by calculating the complement probability of getting no tails, meaning all three tosses are heads. The probability of getting heads three times in a row is (1/2) multiplied by (1/2) multiplied by (1/2), which equals 1/8. Using the complementary event rule, we subtract this from 1 to get 1 - 1/8 = 7/8.

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