# In a lottery of 50 tickets, 8 are winning. What is the probability that among the first 5 randomly

August 17, 2021 | education

| **In a lottery of 50 tickets, 8 are winning. What is the probability that among the first 5 randomly selected tickets there will be no winning ones.**

All outcomes when 5 tickets are drawn out of 50:

n = C (50.5) = 50! / (5! (50 – 5)!) = 46 47 48 49 50 / (1 2 3 4 5) = 2118760;

The number of favorable outcomes, such that there are no winning tickets out of 5, is equal to the number of ways to extract zero tickets out of 8 winning ones, multiplied by the number of ways to get 5 tickets without winning out of 42:

m = C (8.0) C (42.5) = 1 42! / (5! · (42 – 5)!) = 1 · 38 · 39 · 40 · 41 · 42 / (1 · 2 · 3 · 4 · 5) = 850668;

The probability that there will be no winning tickets among 5 tickets:

P = m / n = 850668/2118760 = 0.40149.

Answer: 0.40149.