#### Q. No. 2 :

Two dice are rolled. We define s as the sum of the values on the two faces.

(a) What is the mean (expected value) of s?

(b) What is the probability that s is even?

#### Answer :

(a)Mean is the average value.

Each die can have a value 1 to 6.

Hence the sum can be 2 to 12.

11

12

13

14

15

16

21

22

23

24

25

....

....

....

64

65

66

Hence there are 36 possible combinations.

The total sum can be 252.

Hence the mean is 252/36 = 7

The python code is given below :

```
```

`n = 0`

sum=0

for first in range(1,7):

for second in range(1,7):

sum+=int(first)+int(second)

n+=1

print (int(sum)/n)

(b)

The answer to this problem is rather simple. Among the total combinations possible, half are odd and half are even (As the numbers are sequentially increasing). Hence, the answer is 1/2 = 0.5

```
sum=0
```

n=0

tries=0

for first in range(1,7):

for second in range(1,7):

sum=int(first)+int(second)

if sum%2 ==0 :

n+=1

tries+=1

print(int(n)/tries)

## 0 comments:

## Post a Comment