DICE BASED PROBLEM
Q.
For such experiments, the empirical probability can be applied to events associated with it.
A die is rolled three times.
Find the probability that the sum of three numbers is 15.
Sol:
Given that a die is rolled three times
∴ The no. of outcomes n(s) = 6
3
= 216
Let E be the event of getting a sum of the three numbers is 15.
∴ E = {(3, 6, 6), (4, 5, 6), (4, 6, 5), (5, 5, 5), (5, 6, 4), (5, 4, 6), (6, 3, 6), (6, 6, 3), (6, 5, 4) (6, 4, 5)}
⇒ n(E) = 10
∴ Required probability is
P(E) =
Short-cut method:
A die is rolled 3 times then n(s) = 216
If a die is rolled 3 times, then the number of favourable cases to get the sum 15 =
(20 – 15) (19 – 15)
=
(5) (4) = 10 (∵ from (ii))
∴ Required probability =