mike claims that the probability of winning a pick 6 number game where six numbers are drawn from the set 1 through 49 is about the same as getting 24 heads in a row when you flip a fair coin
1. find the probability of winning the pick 6 game and the probability of getting 24 heads in a row when you flip a fair coin.
i do not get this?!
prob of winning 6/49
= 1/(C(49,6)) = 1/13983816 = .000000071
prob of throwing 24 heads in a row
= (1/2)^24 = 1/16777216 = .000000059
To find the probability of winning a pick 6 number game, where six numbers are drawn from the set 1 through 49, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
In a pick 6 game where six numbers are drawn from a set of 49, the total number of outcomes is given by the combination formula, also known as "49 choose 6":
Total number of outcomes = C(49, 6) = 49! / (6! * (49-6)!)
Number of favorable outcomes:
To win the pick 6 game, one must match all six of the numbers drawn. The number of favorable outcomes is simply 1, since there is only 1 winning combination.
Therefore, the probability of winning the pick 6 game is:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 1 / C(49, 6)
On the other hand, to find the probability of getting 24 heads in a row when you flip a fair coin, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
When flipping a fair coin, there are 2 possible outcomes for each flip - heads or tails. So, the total number of outcomes for 24 coin flips is 2^24.
Number of favorable outcomes:
To get 24 heads in a row, we need to consistently get heads on each of the 24 coin flips. As each flip of the coin is independent, the probability of getting a head on a single flip is 0.5 (if the coin is fair). Therefore, the number of favorable outcomes is simply 1.
Hence, the probability of getting 24 heads in a row when flipping a fair coin is:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 1 / 2^24
Now, to compare the probabilities, you can calculate the values of both probabilities using their respective formulas.