Question

Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding the given integers. (Enter the value of probability in decimals. Round the answer to two decimal places.)

Answer 1

Answer:

(a) 0.35

(b) 0.43

(c) 0.49

(d) 0.54

Step-by-step explanation:

The complete question is:

Find the probability of selecting none of the correct six integers in a lottery, where the order in which these integers are selected does not matter, from the positive integers not exceeding a) 40. b) 48. c) 56. d) 64.

Solution:

(a)

There are n = 40 positive integers.

Compute the probability of selecting none of the correct six integers in a lottery as follows:

$P(\text{0 Correct integers})=\frac{{6\choose 0}\cdot {34\choose 6}}{{40\choose 6}}=\frac{1344904}{3838380}=0.35038\approx 0.35$

(b)

There are n = 48 positive integers.

Compute the probability of selecting none of the correct six integers in a lottery as follows:

$P(\text{0 Correct integers})=\frac{{6\choose 0}\cdot {42\choose 6}}{{48\choose 6}}=\frac{5245786}{12271512}=0.42748\approx 0.43$

(c)

There are n = 56 positive integers.

Compute the probability of selecting none of the correct six integers in a lottery as follows:

$P(\text{0 Correct integers})=\frac{{6\choose 0}\cdot {50\choose 6}}{{56\choose 6}}=\frac{15890700}{32468436}=0.48942\approx 0.49$

(d)

There are n = 56 positive integers.

Compute the probability of selecting none of the correct six integers in a lottery as follows:

$P(\text{0 Correct integers})=\frac{{6\choose 0}\cdot {58\choose 6}}{{64\choose 6}}=\frac{40475358}{74974368}=0.53986\approx 0.54$