What is the probability that in three consecutive rolls of two fair dice, a person gets a total of 7, followed by a total of 11, followed by a total of 7?
*Round to the nearest ten thousandth.
*Round to the nearest ten thousandth.
2 Answers
Explanation:
Let us consider the first case. We denote the probability of "getting a total of 7 in a throw of 2 fair dices" by
Now, there are 6 outcomes when we throw a dice, so the number of possible outcomes when we throw 2 dices at a time is
Now by observation, we get
They can interchange their position in
Hence
Let us consider the 2nd case. We denote the probability of "getting a total of 11 in a throw of 2 fair dices" by
Now, there are 6 outcomes when we throw a dice, so the number of possible outcomes when we throw 2 dices at a time is
Now by observation, we get
They can interchange their position in
Hence
Let us consider the 3rd case. It is the same as the first case, hence
The required probability asked in the question is
The events A, B, C are independent, so
Explanation:
A possibility space is a good way of showing the possible outcomes when two dice are rolled:
There are
There are