Question

A $1 scratch-off lotto ticket will be a winner one out of five times. Out of a shipment of n = 190 lotto tickets, find the probability for the lotto tickets that there are

a) Exactly 35 winning tickets.
b) More than 40 winning tickets.
c) Less than 25 winning tickets.
d) Between 30 and 40 winning tickets.

Answer 1

To find the probability for the lotto tickets, we can use the binomial distribution formula. The probabilities for exactly 35 winning tickets, more than 40 winning tickets, less than 25 winning tickets, and between 30 and 40 winning tickets can be calculated using the binomial distribution formula.

Step-by-step explanation:

To find the probability for the lotto tickets, we can use the binomial distribution formula:

P(X=k) = C(n, k) * p^k * (1-p)^(n-k)

Where:

• P(X=k) is the probability of exactly k winning tickets
• C(n, k) is the number of ways to choose k winning tickets out of n
• p is the probability of winning a single ticket, which is 1/5
• (1-p) is the probability of losing a single ticket, which is 4/5

a) For exactly 35 winning tickets:

P(X=35) = C(190, 35) * (1/5)^35 * (4/5)^(190-35)

b) For more than 40 winning tickets:

P(X>40) = P(X=41) + P(X=42) + ... + P(X=190)

c) For less than 25 winning tickets:

P(X<25) = P(X=0) + P(X=1) + ... + P(X=24)

d) For between 30 and 40 winning tickets:

P(30<X<40) = P(X=31) + P(X=32) + ... + P(X=39)