Probability of Winning Lotto: Calculating E6, E5, En

In summary, the game of 'Lotto' involves 49 distinct numbered balls and a draw of 6 main balls and 1 bonus ball. To win a prize, a player must match a certain number of main balls. The probability of matching all 6 main balls is the same as the probability of flipping two identical coins or rolling two identical dice. The probability of matching 6 particular balls in a draw is p, and the probability of making the same draw as the assistant is also p. For (b) and (c), the probabilities depend on the number of main balls matched, with (b) requiring 5 main balls plus the bonus ball, and (c) requiring any n main balls out of 5,
  • #1
sara_87
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In ‘Lotto’ (a National Lottery game) there are 49 balls, each having a distinct number from the set
S = {1, 2, . . . , 49}. A draw consists of randomly choosing six ‘main’ balls followed by one ‘bonus’
ball. To play the game you choose six distinct numbers from S before the draw, and you win a
prize if any of the following events occur. Calculate the probability of each.
(a) E6: your choice matches all six main numbers;
(b) E5 : your choice matches any five main numbers plus the bonus ball;
(c) En: your choice matches any n main numbers, for n = 5, 4 and 3;

for part (a), i know the sample space is '49 choose 6' but what is the event space?
and i don't know how to do the other two, can someone help please?
thank you
 
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  • #3
it's very interesting...i like it but i still can't figure out how to do it
 
  • #4
For (a), think of the simple experiment where two coins are flipped. What is the probability that they match? Next, think of the experiment where two dice are rolled. What is the probability that they match?

What is the common principle in these two experiments?

Suppose the 6 main balls have been drawn. You know this, but do not know their values. What is the probability that 6 particular balls have been drawn? Let that probability be p. What is the probability that you will make the same draw? What is the probability that both the lottery assistant and you will make this same draw?
 

1. How is the probability of winning Lotto calculated?

The probability of winning Lotto is calculated by dividing the number of possible winning combinations by the total number of possible combinations. For example, in a 6/49 Lotto game, there are 13,983,816 possible combinations. Therefore, the probability of winning the jackpot is 1 in 13,983,816.

2. What is the formula for calculating the probability of winning Lotto?

The formula for calculating the probability of winning Lotto is: P = 1 / C, where P is the probability and C is the total number of possible combinations.

3. What is the probability of winning Lotto if I play multiple tickets?

If you play multiple tickets in the same draw, the probability of winning increases. For example, if you play 10 different tickets in a 6/49 Lotto game, your chances of winning the jackpot become 10 in 13,983,816, which is approximately 1 in 1.4 million.

4. How does the number of balls and numbers selected in Lotto affect the probability of winning?

The number of balls and numbers selected in Lotto directly affects the probability of winning. As the number of balls and numbers increase, the probability of winning decreases. For example, in a 6/49 Lotto game, the probability of winning is lower than in a 5/35 Lotto game.

5. Is there a way to increase my chances of winning Lotto?

Technically, there is no guaranteed way to increase your chances of winning Lotto. However, you can increase your chances by playing more tickets, joining a lottery pool, or choosing numbers that are not commonly picked by other players. Keep in mind that the probability of winning remains the same regardless of the method used.

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