Lauren Mullins

2022-02-14

f two dice are rolled once and one die rolled a second time if the first two rolls have same number, what is the probability of getting a sum of 14?

Evie French

Work backwards, then determine the probabilities
Explanation:
If the sum is 14, then possible values for the second roll (given that the first two are equal) and the value of the first rolls:
(First double, Second single)
$\left(6-6,2\right)$
$\left(5-5,4\right)$
$\left(4-4,6\right)$
P(two 6's then a 2) $={\left(\frac{1}{6}\right)}^{3}=\frac{1}{216}$
Same probability for the other two outcomes.
Total probability $=\frac{3}{216}=\frac{1}{72}$

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