Suppose a fair six-sided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled a second time. What is the probability that the sum total of values that turn up is at least 6?
Suppose a fair six-sided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled a second time. What is the probability that the sum total of values that turn up is at least 6? Correct Answer 5/12
The correct answer is "option 2".
EXPLANATION:
Value on the die for the first time:
{1, 2, 3}
Value on the die for the second time:
{1, 2, 3, 4, 5, 6}
Therefore, values are:
|
First value =1 |
(1,1) |
(1,2) |
(1,3) |
(1,4) |
(1,5) |
(1,6) |
|
Sum |
2 |
3 |
4 |
5 |
6 |
7 |
|
First value =2 |
(2,1) |
(2,2) |
(2,3) |
(2,4) |
(2,5) |
(2,6) |
|
Sum |
3 |
4 |
5 |
6 |
7 |
8 |
|
First value =3 |
(3,1) |
(3,2) |
(3,3) |
(3,4) |
(3,5) |
(3,6) |
|
Sum |
4 |
5 |
6 |
7 |
8 |
9 |
Sample space = 36
The sum must be at least 6 so,
Values of dice are: (1,5), (1,6), (2,4), (2,5), (2,6), (3,3), (3,4), (3,5), (3,6)
So, 9/36 is the probability of getting 6 when both dices are thrown.
If the value of dice comes to 6 in the first dice then there is no need to roll it again.
Prob. of getting 6 is: 1/6
Total probability = 1/6 + 9/36
= 5/12
Hence, the correct answer is “option 2”.
