Question

In Canada’s national 6-49 lottery, a ticket has 6 numbers each from 1 to 49, with no repeats. Find the probability of matching exactly 4 of the 6 winning numbers if the winning numbers are all randomly chosen.

Answer 1

Given:

In Canada's national 6-49 lottery, a ticket has 6 numbers each from 1 to 49, with no repeats.

We solve the given problem by using combination formula.

nCr = n!/(n-r)!r!

The number of way choosing 6 numbers each from 1 to 49, with no repeats is

49C6 = 49!/(49-6)!6! = 49!/43!6! = 13983816

The total number of events with 4 matches is

(6C4) * (43C2) = 6!/(6-4)!4! * 43!/(43-2)!2!

= 6!/2!4! * 43!/41!2! = 13545

Probability = number of favourable events / total number of events

The probability of matching exactly 4 of the 6 winning numbers if the winning numbers are all randomly chosen = 13545 / 13983816 = 0.00097

Therefore the probability of matching exactly 4 of the 6 winning numbers if the winning numbers are all randomly chosen is 0.00097