There are 3 lucky tickets among 10 lottery tickets. 3 tickets are
drawn at random. What is a probability that one ticket selected randomly
from those three is lucky?
PLEASE HELP
To find the probability that one ticket selected randomly from the three drawn tickets is lucky, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Total number of outcomes:
When 3 tickets are drawn randomly from a set of 10, the total number of possible outcomes can be calculated using combinations. The formula for combinations is nCr = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items chosen.
In this case, there are 10 tickets and we are selecting 3, so the total number of possible outcomes is:
10C3 = 10! / (3! * (10 - 3)!)
= 10! / (3! * 7!)
= (10 * 9 * 8) / (3 * 2 * 1)
= 120
Favorable outcomes:
Out of the 10 tickets, there are 3 lucky tickets. So, the number of favorable outcomes is simply 3.
Now, we can calculate the probability using the formula:
Probability (P) = Number of favorable outcomes / Total number of possible outcomes
P = 3 / 120
= 1 / 40
Therefore, the probability that one ticket selected randomly from those three is lucky is 1/40.