Question

Two unbiased dice are rolled once. What is the probability of getting a sum less than 10?

Answer 1

Hint: First we list down all the possibilities of outcomes when two dice are rolled, then we list down all the possibilities which give a sum of less than 10. Then we compute using the formula of probability.

Complete step-by-step answer:

Given, two unbiased dice
Sum less than 10.
When two unbiased dice are rolled once (let this be an event S), the total possible outcomes are
S = {(1,1),(1,2),...(1,6),(2,1),...(2,6),(3,1),..(3,6),.....,(6,6)}
∴n(S) = 6 × 6 = 36 outcomes.
Let A be the event of getting a sum less than 10 when two dice are rolled,
A = {(1,1),(1,2),...(1,6),(2,1),....,(2,6),(3,1),...(3,6),(4,1),...,(4,5),(5,1),(5,4),(6,1),(6,2),(6,3)}
∴n(A) = 30.
Now Probability of sum less than 10, P(A) = $\dfrac{{{\text{n}}\left( {\text{A}} \right)}}{{{\text{n}}\left( {\text{S}} \right)}} = \dfrac{{30}}{{36}} = \dfrac{5}{6}$

Hence, the probability of getting a sum less than 10 when two unbiased dice are rolled is$\dfrac{5}{6}$.

Note: In order to solve this type of questions the key is to carefully list out all the possible outcomes and put it in probability formula which is$\dfrac{{{\text{total number of favorable outcomes}}}}{{{\text{total outcomes}}}}$. Also, a six-sided die is said to be unbiased if it is equally likely to show any of its six sides. When an unbiased dice is thrown the sample space is S = {1, 2, 3, 4, 5, 6}, total number of outcomes = 6.