A pair of fair dice is thrown independently four times. The probability of getting a score of exactly 9 twice is m/9n
then find In - 2ml, where m, n are co-prime.
Answers
Given : A pair of fair dice is thrown independently four times. The probability of getting a score of exactly 9 twice is m/9n
To find : | n - 2m |
Solution:
A pair of fair dice is thrown
Total possible out come = 36
n(S) = 36
Sum 9 = (3 , 6) , ( 4 , 5} , ( 5 , 4) , ( 6 , 3)
n(E) = 4
P(E) = 4/36 = 1/9
p = 1/9
q = 1 - 1/9 = 8/9
Dice thrown 4 times
n = 4
getting a score of exactly twice => x = 2
P(x) = ⁿCₓpˣqⁿ⁻ˣ
=> P(2) = ⁴C₂(1/9)²(8/9)²
= 6 * 8² / 9⁴
= 6 * 64 / 9 * 81 * 9
= 2 * 64 / 9 * 81 *3
= 128 / 9 * 243
Comparing with m/9n
m = 128
n = 243
| n - 2m |
= | 243 - 2 * 128 |
= | 243 - 256 |
= | - 13 |
= 13
| n - 2m | = 13
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