Question

A pair of dice is rolled a 1000 times. The results are as shown.

$\begin{array}{ccccccc}& 1& 2& 3& 4& 5& 6\\ 1& 34& 26& 23& 28& 36& 30\\ 2& 25& 35& 20& 33& 20& 23\\ 3& 25& 27& 36& 23& 23& 30\\ 4& 30& 32& 24& 35& 23& 31\\ 5& 33& 28& 30& 25& 20& 26\\ 6& 26& 35& 21& 28& 25& 31\end{array}$

(i) What is the probability of getting a double?
(ii) What is the probability of getting a 6 on at least one of the two dice?
(iii) What is the probability of getting a 6 on exactly one dice? [4 MARKS]

Answer 1

Concept: 1 Mark
Solution: 1 Mark each

(i) A double is when you get the same value on both dice. In the table given, these values are in the leading diagonal.
Number of times we got a double = 34 + 35 + 36 + 35 + 20 + 31 = 191
Probability of getting a double =$\frac{191}{1000}=0.191$.

(ii) To get a 6 on at least one of the two dice, we select the elements on the sixth row and the sixth column. There are a total of 11 elements because one is common to both the sixth row and the sixth column.
Number of times we got a six on at least one of the two dice = 26 + 35 + 21 + 28 + 25 + 31 + 26 + 31 + 30 + 23 + 30 = 306

Probability of getting a 6 on at least one of the two dice=$\frac{306}{1000}=0.306$.

(iii) To get a 6 on exactly one of the two dice, we must select elements which are on the sixth row or the sixth column, but not on both. Thus, we have 10 elements.
Number of times we get a six on exactly one of the two dice = 26 + 35 + 21 + 28 + 25 + 26 + 31 + 30 + 23 + 30 = 275

Probability of getting a 6 on exactly one dice =$\frac{275}{1000}=0.275$.