To win a particular lottery game a player chooses 5 numbers from 0 to 63. If all five numbers that the player selected match the winning numbers in any order, then the player wins. What is the probability that the winning numbers are 7, 0, 29, 45, and 60?

Question

Madeline Alexander · Accepted Answer

There are 64 numbers and since the order of the numbers does not matter , this is a combination problem ...

Sample Space #=(64!)/(5!xx59!)=7,624,512# possible combinations! P{7, 0, 29, 45, and 60} #=1/(7,624,512)~~1.3xx10^-7# hope that helped

Audrey Allen · Answer

undefined The probability of winning the lottery game with the specific numbers 7, 0, 29, 45, and 60, regardless of the order chosen, can be calculated as follows:

1. Determine the total number of possible combinations of choosing 5 numbers from the range 0 to 63, which is given by the combination formula:
   $$ \text{Total combinations} = \binom{64}{5} $$

2. Calculate the number of favorable outcomes, which is 1 since there is only one specific combination of winning numbers.

3. Use the formula for probability:
   $$ \text{Probability of winning} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} $$

Substitute the values into the formula to find the probability.

$$ \text{Probability of winning} = \frac{1}{\binom{64}{5}} $$

You can then calculate the numerical value of this expression to find the probability.