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Addition Theorem of Probability for 2 Events

Two dice are ...

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 42
5 55
6 72
7 75
8 70
9 53
10 46
11 28
12 15
What is the probability of getting a sum:
Less than or equal to 5?

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Solution

Two dice are thrown $500$ times. So, the total number of trials are $500$ .

Let $E_{3}$ be the event that sum of two numbers appearing on the uppermost faces of two dice be less than or equal to $5$ .

Number of times in which the event happed $= 14 + 30 + 42 + 55 = 141$

$∴ P (E_{3}) = \frac{N u m b e r o f t r a i l s i n w h i c h t h e e v e n t h a p p e d}{T o t a l n u m b e r o f t r a i l s}$

$= \frac{141}{500} = 0.282$

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Q. 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.
What is the probability of getting a sum:

Sum	Frequency
2	14
3	30
4	42
5	55
6	72
7	75
8	70
9	53
10	46
11	28
12	15

Q. 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	42
5	55
6	72
7	75
8	70
9	53
10	46
11	28
12	15

What is the probability of getting a sum:
Between 8 and 12?

Q. 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

\begin{matrix} Sum & Frequency 2 & 14 3 & 30 4 & 42 5 & 55 6 & 72 7 & 75 8 & 70 9 & 53 10 & 46 11 & 28 12 & 15 \end{matrix}

If the dice are thrown once more, then what is the probability of getting a sum
(i) 3?
(ii) More than 10?
(iii) Less than or equal to 5?
(iv) Between 8 and 12?

Q. 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?

Q. 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 between 8 and 12?

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