Question

two dice are thrown simultaneously. find probability that sum is a perfect square​

Answer 1

Step-by-step explanation:

the perfect squares are:

1*1 = 1

2*2 = 4

3*3 = 9

4*4 = 16

5*5 = 25

6*6 = 36

the number of possible products when you throw 2 dice is equal to 6 * 6 = 36

they are:

1*1 = 1 ***

1*2 = 2

1*3 = 3

1*4 = 4 ***

1*5 = 5

1*6 = 6

2*1 = 2

2*2 = 4 ***

2*3 = 6

2*4 = 8

2*5 = 10

2*6 = 12

3*1 = 3

3*2 = 6

3*3 = 9 ***

3*4 = 12

3*5 = 15

3*6 = 18

4*1 = 4 ***

4*2 = 8

4*3 = 12

4*4 = 16 ***

4*5 = 20

4*6 = 24

5*1 = 5

5*2 = 10

5*3 = 15

5*4 = 20

5*5 = 25 ***

5*6 = 30

6*1 = 6

6*2 = 12

6*3 = 18

6*4 = 24

6*5 = 30

6*6 = 36 ***

out of these only 8 generate a perfect square.

the probbility of getting a perfect square is therefore 8/36 = 4/18 = 2/9.

note that there are more possible factors of two number that equal a perfect square, but the highest factor has to be less than or equal to 6 which is the maximum number possible on one 6 sided die.

for example:

16 = 1*16 or 2*8 ot 4*4 or 8*2 or 16*1

out of all these factors, only 1 is possible, which is 4*4.

the only one where all possible factors can be considered is 4.

4 is the product of 1*4 or 2*2 or 4*1.

all these factors are possible when you are throwing 2 die.

Answer 2

Answer:

P(sum is a perfect square)=$\dfrac{7}{36}$

Step-by-step explanation:

We had given that sum of the outcomes must be a perfect square  

the minimum sum would be=1+1=2

the maximum sum would be=6+6=12

So between 2 and 12, 4 and 9 are the only perfect squares

Therefore the outcomes by which we can get 4 and 9 as a sum are:

1+3

3+1

2+2

6+3

3+6

4+5

5+4

These are the total number of outcomes by which we can get the perfect square, These are total 7 possibilities

Therefore we know that the total number of outcomes=36

P(sum is a perfect square)=$\dfrac{7}{36}$