Arjun and Ayaan each roll one dice, numbered from 1 to 6. If P is the probability that Ayaan gets a higher number than Arjun, then find 24P.
Answers
Given : Arjun and Ayaan each roll one dice, numbered from 1 to 6. P is the probability that Ayaan gets a higher number than Arjun
To find : 24P.
Solution:
Arjun and Ayaan each roll one dice, numbered from 1 to 6.
Total possible ways = 6 * 6 = 36
Ayaan gets a higher number than Arjun,
Arjun Ayaan
1 2 , 3 , 4 ,5 , 6
2 3 , 4 ,5 , 6
3 4 ,5 , 6
4 5 , 6
5 6
Total Ways = 5 + 4 + 3 + 2 + 1 = 15
Probability that Ayaan gets a higher number than Arjun,
= 15/36
= 5/12
24P = 24 (5/12 )
= 10
24P = 10
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Assuming the dice considered is a fair dice without any faults.
Given, Arjun and Ayaan each roll one dice, numbered from 1 to 6.
Total outcomes = 6*6=36
As per the requirement, there will be 6 instances if a tie occurs - {(1,1) (2,2) (3,3) (4,4) (5,5) (6,6)}
Total possible ways = 5 + 4 + 3 + 2 + 1 = 15
So, here we calculate
P= No. of rolls in which Ayaan has probability of winning
P = 15/36
P = 5/12
Now 24P = 24* 5/12 = 10= 10
24P = 10 is the required answer.
Hope it helps!
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