In a lottery game, a player picks six numbers
from 1 to 48. If 5 of the 6 numbers match those
drawn, they player wins second prize. What is
the probability of winning this prize? �
To find the probability of winning the second prize in the lottery game, we need to determine the number of favorable outcomes (which is winning the second prize) and the total number of possible outcomes (which is all the number combinations that can be drawn).
The number of favorable outcomes is finding the number of ways to choose 5 correct numbers out of 6. This can be calculated using the combination formula, which is:
C(n, k) = n! / (k! * (n - k)!)
Where n represents the total number of choices (48 in this case), and k represents the number of choices we want to make (5 in this case).
C(48, 5) = 48! / (5! * (48 - 5)!)
Simplifying the equation:
C(48, 5) = 48! / (5! * 43!)
Similarly, the total number of possible outcomes can be calculated as choosing any 6 numbers out of the 48:
C(48, 6) = 48! / (6! * (48 - 6)!)
Simplifying the equation:
C(48, 6) = 48! / (6! * 42!)
The probability of winning the second prize is the ratio of the number of favorable outcomes to the total number of possible outcomes:
P(win second prize) = C(48, 5) / C(48, 6)
Now, we can calculate the probability using the given values and formulas.