in a certain, lottery five different numbers between 1 and 35 inclusive and drawn. these are the winning numbers. to win the lottery, a person must select the 5 correct numbers in the same order in which they were drawn. what is the probability of winning.
The probability of winning the lottery is 1 in 2,118,760.
To calculate the probability of winning the lottery, we need to determine the number of possible outcomes and the number of favorable outcomes.
Number of possible outcomes:
Since there are 35 numbers to choose from for each of the 5 positions, there are a total of 35 choices for the first position, 34 choices for the second position, 33 choices for the third position, 32 choices for the fourth position, and 31 choices for the fifth position. Therefore, the number of possible outcomes is calculated as follows:
35 * 34 * 33 * 32 * 31 = 654,450
Number of favorable outcomes:
Since the numbers need to be selected in the same order as they were drawn, there is only one favorable outcome, which is the specific combination of numbers drawn.
Now we can calculate the probability of winning:
Probability of winning = Number of favorable outcomes / Number of possible outcomes
Probability of winning = 1 / 654,450
Therefore, the probability of winning the lottery is approximately 1 in 654,450.
To find the probability of winning the lottery, we need to determine the number of possible outcomes and the number of favorable outcomes.
In this case, there are 35 possible numbers for each of the 5 positions. Therefore, the total number of possible outcomes is 35 × 35 × 35 × 35 × 35 = 35^5.
Since the numbers must be selected in the same order as they were drawn, there is only one favorable outcome.
So, the probability of winning the lottery is 1 (favorable outcome) divided by 35^5 (possible outcomes):
Probability = 1 / 35^5
Calculating this probability gives us a very small number, approximately 1 in 3,086,140,625.
Therefore, the probability of winning the lottery is extremely low.