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2 VERSION 3 : MARCH 1, 2003 Winning without the bonus Some of the prize categories for the other jackpots are for matching “4 of the 6 winning numbers” or “3 of the 6 winning numbers.” There are 6 numbers on a ticket which wins these prizes. To match k of the winning numbers, we must select k of 6 winning numbers AND we must select (6 − k) of the 43 non-winning numbers. Therefore there are 6 × 43 possible winning tickets matching k of the winning numbers. probability of having 4 of 6 winning numbers = probability of having 3 of 6 winning numbers = 643 4 2 1 ≈ 1033 k 6−k 6·5·4·3 · 43·42 4·3·2·1 2·1 49 = 6 13983816 6·5·4 · 43·42·41 1 643 3 3 3·2·1 3·2·1 13983816 ≈ 57 49 = 6 There is an exception to this in the condition if we insist that the ticket not include the bonus number (e.g. the prize for “5 of 6 winning numbers and not the bonus” because the tickets with “5 of 6 winning numbers and the bonus” win a bigger prize). In this case, the number of tickets which include k winning numbers AND 6 − k of the 42 non-winning numbers which are not the bonus will be 6 × 42 . 6 k 6−k probability of having 5 of 6 winning numbers and not the bonus = Winning with the bonus 642 51 numbers and the bonus. probability of having 5 of 6 winning numbers and the bonus = 49 6 642 50 61 = 13983816 = 2330636 6·42 1 49 = 13983816 ≈ 55491 The number of tickets which have k winning numbers and the bonus can be found by choosing k of the 6 winning numbers AND the bonus number AND choosing 5 − k of the 42 non-winning/non- bonus numbers. This means that there are 6 × 42 tickets which include exactly k winning k 5−kPDF Image | CALCULATING THE PROBABILITIES OF WINNING LOTTO
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