A box contains 10 balls numbered 1 through 10.Anuj and anisha and amit pick a ball each one after th other each time replacing the ball.What is the probability that anuj picks a ball numbered less than picked by anuisha who in turns picks a lesser numbered than amit?
Answers
The probability may be 3/25
Answer:
The probability is 3 / 25 = 0.12
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Step-by-step explanation:
Let x, y, z be Anuj's, Anisha's and Amit's numbers.
As there are 10 choices for each, total number of possiblities
= 10³ = 1000
Need to count number of choices with x < y < z.
Put a = x, b = y - x, c = z - y, d = 11 - z.
Then if x < y < z, we have four positive integers that add up to 11.
And if we give a, b, c, d four positive integer values that add up to 11, then that gives a choice with x < y < z.
So
# of choices with x < y < z
= # ways to write 11 = a + b + c + d with positive integers
= # ways to choose 3 spaces from 10 spaces (in a row of eleven 1's) where to put a "+" sign
= ( 10 × 9 × 8 ) / ( 3 × 2 × 1 )
= 720 / 6
= 120
Therefore,
Prob( x < y < z )
= ( # of choices with x < y < z ) / ( # total number of possibilities )
= 120 / 1000
= 3 / 25