I represent a charity, that runs a standard Bingo game weekly. A typical game sh
ID: 3171603 • Letter: I
Question
I represent a charity, that runs a standard Bingo game weekly. A typical game sheet is attached, which includes 4 game cards. (The minimum purchase is 1 sheet, consisting of 4 cards)
There are 4500 sheets printed (therefore 18,000 cards) and distributed; not all may be sold in any given week.
The top prize of $2,500 is awarded for a full card (all numbers on the winning card are called) to the first player who 'bingo's'. i.e. the game continues to be played until there is a bingo/full card. However, if the player bingo's on 48 numbers or less, the prize is $4,000.
Required: what is the probability of a full card on 48 numbers or less? If all 4500 sheets are sold (and therefore played)? If 3000 sheets are sold? (since normally not all sheets are sold).
Note: the key is that we need to know the likelihood or probability of there being a winner on a full card, if 48 numbers or less are called. There can only be ONE winner per game (i.e. the first player to have a full card)
B 6660003 G O E3 6660003 G O PRINTED IN U.S.A. ARROW INTL 1989 1989 ARAOUU INTL PAINTED IN U.S.A 7 26 34 54 70 3 24 38 48 69 8 19 33 51 68 5 16 33 55 63 21 57 FREE 15 24 36 49 75 4 18 39 54 65 13 18 38 50 62 7 30 45 47 61 R, 1301 12051 12001 B 6660003 GG CO B 6660003 G GO PRINTED IN C ARROW INTL 1989 PRINTED IN U.S.A. ARROW INTL 1989 2 17 40 50 64 7 24 35 47 71 1116 3151 70 8 20 33 51 63 FREE 7 25 53 75 2 16 FREE 50 69 8 28 33 60 68 3 17 42 56 61 3901 1951 39 49 61 R 9 23 43 58 12351 5 651 12301 68 3001Explanation / Answer
On a card there are total 24 numbers. In order to have a Bingo on the number 48 or less, 24 numbers to be selected from the first 48 numbers.
24 numbers from the first 48 numbers can be selected in 48C24 ways.
Total possible ways to form a card from the first 100 numbers (00 - 99), 100C24.
Hence probability of winning card such that winning numbers are 48 or less = 48C24/100C24 = 4/10^10 (lets consider this value as p)
If all 4500 sheets are sold i.e. 18000 cards, probability that of winner with 48 or less numbers is
18000C1 * p^1 * (1-p)^17999 = 7.28 * 10^-6
If only 3000 sheets are sold i.e. 12000 cards, probability that of winner with 48 or less numbers is
12000C1 * p^1 * (1-p)^11999 = 4.85 * 10^-6