Question
A black die and a white die are thrown at the same time. Write all the possible outcomes. What is the probability?
That the sum of the two numbers that turn up is $7?$
That the sum of the two numbers that turn up is $7?$
✓
Answer
Given: A pair of dice is thrown
To Find: Probability of the following:
Let us first write the all possible events that can occur
Favorable events i.e. getting the sum of numbers on the dice equal to $8$
$(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)$
Hence total number of favorable events i.e. the sum of numbers on the dice equal to $8$ is $5$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability of getting the sum of numbers on the dice equal to $8=\frac{5}{36}$
To Find: Probability of the following:
Let us first write the all possible events that can occur
$(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),$
$(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),$
$(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),$
$(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),$
$(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),$
$(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),$
Hence total number of events is $6^2= 36$Favorable events i.e. getting the sum of numbers on the dice equal to $8$
$(2, 6), (3, 5), (4, 4), (5, 3), (6, 2)$
Hence total number of favorable events i.e. the sum of numbers on the dice equal to $8$ is $5$
We know that $\text{Probability}=\frac{\text{Number of favourable event}}{\text{Total number of event}}$
Hence probability of getting the sum of numbers on the dice equal to $8=\frac{5}{36}$
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