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

Beginner2022-02-15Added 18 answers

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)

$(6-6,2)$

$(5-5,4)$

$(4-4,6)$

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$=\frac{3}{216}=\frac{1}{72}$

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)

P(two 6's then a 2)

Same probability for the other two outcomes.

Total probability