Question

Two dice are thrown simultaneously 500 times. Each time the sum of two numbers appearing on their tops is noted and recorded as given in the following table:

Sum	Frequency
2	14
3	30
4	43
5	55
6	72
7	75
8	70
9	53
10	46
11	28
12	15

If the dice are thrown once more, what is the probability of getting a sum more than 10?
A.\[0.05\]
B.\[0.063\]
C.\[0.08\]
D.\[0.086\]

Answer 1

Hint: Here we need to find the probability of getting a sum more than 10. For that, we will first find the probability of getting a sum of 11 which will be equal to the ratio of corresponding frequency to the number of times the dice are thrown. Then we will find the probability of getting a sum of 12 which will be equal to the ratio of corresponding frequency to the number of times the dice are thrown. We will then combine these probabilities together to get the required frequency.

Complete step-by-step answer:
It is given that:
Number of times the dice thrown \[ = 500\]
 Here we have to find the probability of getting a sum more than 10.
We will first find the probability of getting a sum of 11 which will be equal to the ratio of corresponding frequency to the number of time the dice are thrown
We can see from the table that the frequency corresponding to the sum of 11 is 28.
Therefore,
Probability of getting a sum of 11 \[ = \dfrac{{28}}{{500}}\]
Similarly, we will now find the probability of getting a sum of 12 which will be equal to the ratio of corresponding frequency to the number of time the dice are thrown
We can see from the table that the frequency corresponding to the sum of 12 is 15.
Therefore,
Probability of getting a sum of 12 \[ = \dfrac{{15}}{{500}}\]
Probability of getting a sum more than 10 is equal to the probability of getting a sum of 11 and probability of getting a sum of 12.
Therefore,
Probability of getting sum more than 10 \[ = \dfrac{{28}}{{500}} + \dfrac{{15}}{{500}}\]
On adding these fractions, we get
Probability of getting sum more than 10 \[ = \dfrac{{28 + 15}}{{500}} = \dfrac{{43}}{{500}}\]
On further simplification, we get
 Probability of getting sum more than 10 \[ = 0.086\]
Hence, the correct option is option D.

Note: To solve such a type of problem, we need to know about probability and its properties. Probability is defined as the ratio between the number of desired or favorable outcomes and the total number of possible outcomes. We need to keep in mind that the value of probability cannot be greater than 1 and also cannot be negative. Also the probability of a sure event is always one.