The sorry state lottery requires he does like five different numbers from 0 to 67 you are a big winner is the five numbers you select agree with those in the drawing and you are a small fry wonder if four of your five numbers agree with those in the drawing what is the probability of being a big winner
prob(big winner) = 1/C(68,5)
= 1 / 10,424,128
= appr .000,000,1
To calculate the probability of being a big winner in the lottery given that four out of your five numbers match those in the drawing, we need to consider the total number of possible outcomes and the number of favorable outcomes.
Let's break down the calculation step by step:
Step 1: Determine the total number of possible outcomes.
In this case, you need to select five numbers from a range of 0 to 67. Since each number can be selected independently, the total number of possible outcomes can be found using combinatorial analysis or the formula for combinations. The equation is:
nCr = n! / (r!(n-r)!)
where n is the total number of choices or options and r is the number of choices being made.
Therefore, the total number of possible outcomes in this lottery can be calculated as:
67C5 = 67! / (5!(67-5)!) = (67 * 66 * 65 * 64 * 63) / (5 * 4 * 3 * 2 * 1) = 6,153,760
Step 2: Determine the number of favorable outcomes.
Since you have selected four numbers correctly, you now need to determine the number of ways to choose the remaining number. Since there are 67 numbers to choose from, and you already have one match, there are 66 remaining numbers to choose from for the fifth position.
Therefore, the number of favorable outcomes can be calculated as:
66C1 = 66! / (1!(66-1)!) = 66
Step 3: Calculate the probability.
Finally, we can calculate the probability of being a big winner by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 66 / 6,153,760 ≈ 0.0000107
Therefore, the probability of being a big winner, given that four out of your five numbers match those in the drawing, is approximately 0.0000107 (or 1 in 93,396).