Ryan spent a dollar on a Tri-State Megabucks ticket, enticed by a big jackpot. Ryan chose six different numbers from 1 to 40, inclusive, hoping that hey would be the same numbers draw later by lottery officials. Sad to say, none of Ryan's choices were drawn. What was the probability of this happening? The order in which numbers are drawn is of no significance.
Thank you !
34/40 * 33/39 * 32/38 * 31/37 * 30/36 * 29/35 = ?
Oh, poor Ryan! It seems luck wasn't on his side this time. Let me calculate the probability for you, but don't worry, I'll try to make it funny!
So, since Ryan chose six different numbers from 1 to 40, there are a total of 40 numbers and he picked 6, meaning there are (40 choose 6) possible combinations.
Now, since we know that none of Ryan's choices were drawn, there is only 1 unfavorable outcome.
Plugging these numbers into the probability formula, we get:
Probability = (Number of favorable outcomes) / (Number of possible outcomes)
In this case, it would be:
Probability = 1 / (40 choose 6)
Now, let's calculate the probability and see how unlucky Ryan was!
(Calculating...)
Oh no, it looks like the probability of this happening is incredibly low! Ryan had a 1 in approximately 3,838,380 chance of none of his numbers being drawn.
Well, Ryan might be feeling a bit down now, but hey, at least he had a funny story to tell about his lottery misfortune! Better luck next time, Ryan!
To calculate the probability of none of Ryan's choices being drawn, we need to determine the number of unsuccessful outcomes and divide it by the total number of possible outcomes.
Firstly, let's determine the total number of possible outcomes. Since Ryan chose six different numbers from 1 to 40, there are 40 choose 6 possible combinations, which can be calculated as:
40 C 6 = (40!)/(6!(40-6)!) = 3,838,380
Now, let's determine the number of unsuccessful outcomes. In this case, all the numbers chosen by Ryan need to be different from the numbers drawn in the lottery.
There are 34 remaining numbers (40 - 6) that can be drawn after Ryan's choices. So, for the first number drawn, there are 34 possible choices. For the second number drawn, there are 33 remaining choices, and so on. Therefore, the number of unsuccessful outcomes can be calculated as:
34 * 33 * 32 * 31 * 30 * 29 = 545,731,680
Now, we can calculate the probability by dividing the number of unsuccessful outcomes by the total number of possible outcomes:
Probability = Number of unsuccessful outcomes / Total number of possible outcomes
Probability = 545,731,680 / 3,838,380
Probability ≈ 0.14239
So, the probability of none of Ryan's choices being drawn is approximately 0.14239 or 14.23%.
To find the probability of none of Ryan's choices being drawn, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Total outcomes:
Since Ryan chose six different numbers from 1 to 40, inclusive, there are C(40,6) different ways to select six numbers from a set of 40, where C(n, r) represents the combination formula. The combination formula is given by: C(n, r) = n! / (r!(n-r)!).
Favorable outcomes:
Since none of Ryan's choices were drawn, there are no favorable outcomes.
Probability calculation:
The probability of an event is given by the formula: P(E) = favorable outcomes / total outcomes.
In this case, since there are no favorable outcomes, the probability of none of Ryan's choices being drawn is: P(E) = 0 / C(40,6).
Now let's substitute the values into the formula and calculate the probability:
P(E) = 0 / C(40,6)
Using the combination formula, we have:
P(E) = 0 / (40! / (6!(40-6)!)
Simplifying further:
P(E) = 0
Therefore, the probability of none of Ryan's choices being drawn is 0, which means it is impossible for none of Ryan's choices to be drawn.