In a lottery, person choses six different natural numbers at random from 1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? [ Hint: order of the numbers is not important.]
It is given that, in a lottery, a person chooses six different natural numbers at random from 1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize.
The number of ways in which six different numbers can be chosen between the numbers 1 to 20 is given by,
C 20 6 = 20 ! 6 ! ( 20 − 6 ) ! = 20 ! 6 ! 14 ! = 20 × 19 × 18 × 17 × 16 × 15 1 × 2 × 3 × 4 × 5 × 6 = 38760
So, total possible numbers in sample space is,
n ( S ) = 38760
Out of these 38760 combinations of six numbers, one is already fixed by the lottery committee.
Let A be the event “the person chooses the correct numbers”.
n ( A ) = 1
The probability for winning the lottery is given by,
P ( A ) = number of outcomes favourable to A Total number of outcomes = n ( A ) n ( S ) = 1 38760
Thus, the probability of winning the lottery is 1 38760 .
It is given that, in a lottery, a person chooses six different natural numbers at random from 1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize.
The number of ways in which six different numbers can be chosen between the numbers 1 to 20 is given by,
So, total possible numbers in sample space is,
Out of these 38760 combinations of six numbers, one is already fixed by the lottery committee.
Let A be the event “the person chooses the correct numbers”.
The probability for winning the lottery is given by,
Thus, the probability of winning the lottery is
