A cubical dice is rolled two times. Show the probabilities of all the possible outcomes of getting or not getting 5 in a tree diagram
To show the probabilities of all possible outcomes of rolling a cubical dice two times and getting or not getting a 5, we can use a tree diagram.
The first roll has six possible outcomes, which are represented by the first level branches of the tree diagram.
/ \
/ \
1 2
/ \ / \
/ \ / \
/ \ / \
3 4 5 6
Each branch represents a number that could be rolled on the first roll.
For each branch, there are again six possible outcomes for the second roll, which are represented by the second-level branches of the tree diagram.
/ \
/ \
1 2
/ \ / \
/ \ / \
/ \ / \
3 4 5 6
/ | | | | | \
/ | | | | | \
1..6 1..6 1..6 1..6 1..6 1..6
For each outcome on the second roll, we can add a branch representing whether a 5 was rolled or not. Let's label these branches as "5" for getting a 5 and "Not 5" for not getting a 5.
The final tree diagram will look like this:
/ \
/ \
1 2
/ \ / \
/ \ / \
/ \ / \
3 4 5 6
/ | | | | | \
/ | | | | | \
1..6 1..6 1..6 1..6 1..6 1..6
/ | |
/ | |
5 Not 5 5 Not 5
Now we can assign probabilities to each branch.
Since the rolling of a cubical dice is a fair game or experiment, all the probabilities of obtaining the numbers 1 to 6 in a single roll are equal. So each of the first-level branches will have a probability of 1/6.
For the second-level branches, the probability of obtaining any number from 1 to 6 is also 1/6 for each branch.
For the third-level branches, the probability of getting a 5 is 1/6, and the probability of not getting a 5 is 5/6.
Therefore, we can calculate the probabilities of all possible outcomes by multiplying the probabilities along each path. For example:
The probability of getting a 5 on the first and second rolls is (1/6) * (1/6) = 1/36.
The probability of not getting a 5 on the first roll but getting a 5 on the second roll is (5/6) * (1/6) = 5/36.
By calculating the probabilities along all paths, we can determine the probabilities of all possible outcomes of getting or not getting a 5 when rolling a cubical dice two times.