Multiple choice

A die is thrown four times. The probability of getting perfect square in at least one throw is

  1. $\cfrac { 16 }{ 81 } $
  2. $\cfrac { 65 }{ 81 } $
  3. $\cfrac { 23 }{ 81 } $
  4. $\cfrac { 58 }{ 81 } $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Perfect squares on a die are 1 and 4. Probability of getting a perfect square in one throw = 2/6 = 1/3. Probability of not getting one = 2/3. Probability of not getting one in 4 throws = (2/3)^4 = 16/81. Probability of at least one = 1 - 16/81 = 65/81.

AI explanation

A perfect square on a die is 1 or 4, so the probability of a perfect square is 2/6 or 1/3. The probability of not getting a perfect square in one throw is 2/3. Using the complement rule, the probability of at least one perfect square in four throws is 1 minus (2/3)^4, which is 1 minus 16/81. This equals 65/81.

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