You roll two dice. What is the probability of getting a 3 or a 6 on the second die, given that you rolled a 1 on the first die?

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You roll two dice. What is the probability of getting a 3 or a 6 on the second die, given that you rolled a 1 on the first die?

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Answer 1 · 2018-04-09T11:31:23

$P (3 or 6) = \frac{1}{3}$ $P(3 or 6) =1/3$

Explanation:

Notice that the outcome of the first die does not affect the outcome of the second. We are only asked about the probability of a $3 or 6$ $3or 6$ on the second die.

There are $63$ $63$ numbers on a die, of which we want two - either $3 or 6$ $3 or 6$

$P (3 or 6) = \frac{2}{6} = \frac{1}{3}$ $P(3 or 6) = 2/6 = 1/3$

If you are wanting the probability for both dice, then we have to consider the probability of getting the $1$ $1$ first.

$P (1, 3) or (1, 6) = P (1, 3) + P (1, 6)$ $P(1,3) or (1,6) = P(1,3) +P(1,6)$

$= (\frac{1}{6} \times \frac{1}{6}) + (\frac{1}{6} \times \frac{1}{6})$ $= (1/6 xx 1/6) + (1/6 xx 1/6)$

$= \frac{1}{36} + \frac{1}{36} = \frac{2}{36} = \frac{1}{18}$ $=1/36 +1/36 = 2/36 = 1/18$

We could also have done: $\frac{1}{6} \times \frac{1}{3} = \frac{1}{18}$ $1/6 xx 1/3 = 1/18$

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You roll two dice. What is the probability of getting a 3 or a 6 on the second die, given that you rolled a 1 on the first die?

1 Answer

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