Question

two dice are tossed. find the probability that the sum of the scores on the dice is: a prime number, a multiple of 3,not less than 10,between 4 and 9​

Answer 1

Answer:

1. 5/12  2. 1/36  3. 19/36

Step-by-step explanation:

POSSIBLE OUTCOMES ARE -:

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

1. THERE ARE TOTAL 36 POSSIBLE OUTCOMES. (THE SUMS WHICH LEAD TO PRIME NUMBERS HAVE BEEN UNDERLINED.) THE SUMS/OUTCOMES WHICH LEAD TO PRIME NUMBERS AS THEIR TOTAL ARE 15 IN NUMBER.

THUS, P =    15/36 = 5/12

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

2. AGAIN, THERE ARE 36 POSSIBLE OUTCOMES, OUT OF WHICH 13 LEAD TO THE MULTIPLES OF 3. THUS, P = 12/36 = 1/3

BUT, AS WE HAVE TO FIND THE PROBABILITY OF THOSE WHOSE SUM IS NOT LESS THAN 10, THEN, THE ONLY POSSIBILITY IS (6,6), SO, P = 1/36

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

3. IN THE THIRD CASE, WE SEE THAT THERE ARE 19 POSSIBILITIES FOR THE SAME OUT OF 36 POSSIBILITIES, SO, THE P = 19/36

P = PROBABILITY

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