Respuesta :
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:
[tex]P(\text{0 Correct integers})=\frac{{6\choose 0}\cdot {34\choose 6}}{{40\choose 6}}=\frac{1344904}{3838380}=0.35038\approx 0.35[/tex]
(b)
There are n = 48 positive integers.
Compute the probability of selecting none of the correct six integers in a lottery as follows:
[tex]P(\text{0 Correct integers})=\frac{{6\choose 0}\cdot {42\choose 6}}{{48\choose 6}}=\frac{5245786}{12271512}=0.42748\approx 0.43[/tex]
(c)
There are n = 56 positive integers.
Compute the probability of selecting none of the correct six integers in a lottery as follows:
[tex]P(\text{0 Correct integers})=\frac{{6\choose 0}\cdot {50\choose 6}}{{56\choose 6}}=\frac{15890700}{32468436}=0.48942\approx 0.49[/tex]
(d)
There are n = 56 positive integers.
Compute the probability of selecting none of the correct six integers in a lottery as follows:
[tex]P(\text{0 Correct integers})=\frac{{6\choose 0}\cdot {58\choose 6}}{{64\choose 6}}=\frac{40475358}{74974368}=0.53986\approx 0.54[/tex]
Probability of selecting none of the six integers in a lottery is 0.35
Probability based problem:
Assuming that number n = 40.
n = 40 as a positive integer
Probability of selecting none of the correct six integers in a lottery = C(34 , 6) / C(40 , 6)
Probability of selecting none of the correct six integers in a lottery = 1344904 / 3838380
Probability of selecting none of the correct six integers in a lottery = 0.35
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