Question

A fair die is rolled two times. What is the probability that both rolls are 3?

Answer 1

Answer:

1/36

Step-by-step explanation:

For each roll, the probability that the die rolls a 3 is 1/6

So, for it to happen on both dice is 1/6 * 1/6 = 1/36

Answer 2

The probability that an event will repeat its self for independent events is given by the square of the probability of the event occurring

• The probability that both rolls are 3s is  $\underline{\dfrac{1}{36}}$

Reason:

Number of faces in a fair die = 6 faces

Numbers on the faces of a fair die = 1, 2, 3, 4, 5, and 6

Number of 3s on the face of a fair die = 1

Probability that a roll of a fair die gives the face of 3, P(3) = $\dfrac{1}{6}$

The probability that two rolls of a fair die are both, is given as follows;

P(Both 3) = P(3 and 3) = P(3 ∩ 3)

The and condition of two independent probabilities is the product of the two probabilities, therefore;

P(3 ∩ 3) = $\dfrac{1}{6} \times \dfrac{1}{6} = \dfrac{1}{36}$

The probability that both rolls are 3s P(Both 3s) = $\underline{\dfrac{1}{36}}$

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