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
Answers
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
DISCLAIMER -: I DO NOT HOLD THE RESPONSIBILITY FOR ANY WRONG INFORMATION SPREAD FROM THIS. I HAVE TRIED MY LEVEL BEST TO EXPLAIN THE ANSWERS AS WELL AS PROVIDE ACCURATE INFORMATION. BUT, IF THERE IS ANY MISTAKE, I DO NOT HOLD RESPONSIBILITY FOR ANY DAMAGE TO ANYTHING OR WHATSOEVER. HOPE THIS ANSWER PROVES HELPFUL. IF THERE IS ANY FLAW, THEN, PLEASE POINT IT OUT IN THE COMMENTS.
THANK YOU!
HAVE A GOOD DAY!