A group of 30 students from your school is part of the audience for a TV game show. The total number of people in the audience is 120. What is the theoretical probability of 5 students from your school being selected as contestants out of 8 possible contestant spots?
Answers
Answer:
In general, probably can be found as n(E)/n(S), where n(E) is the number of favorable outcomes, and n(S) is the number of total outcomes.
n(S) is the number of ways any 9 students can by picked from the audience, which is 9/140.
n(E) is the probability of picking four students from our school and five students from another school. This is (4/30)*(5/110) = 9/3300 =3/1100
n(E)/n(S) = (3/1100) / (9/140) = (3/1100) * (140/9) = 14/330
Answer:
5.3%
Step-by-step explanation:
The final probability is calculated by means of the quotient of the specific combination and the total of total combinations
Let's start with the specific ones,
First the no. of combination of 4 of the 30 students getting a spot, i.e..
A combination are equal to:
nCx = n! / n! * (n-x)!
Replacing:
30C4 = 30! / (4! *26) = 27405
Segundo the no. of combination of the other audience members filling the other 4 (8-4)spots n = 110,140-30
110C4 = 110! / (4!*106!)=5773185
Now the total combination of possible 8 contestants from the audience
140C8=140!/(8!*132!) = 2.98*10^12
Finally, the probability is equal to:
P = (30C4*110C4)/140C8
Replacing:
P = 27405*5773185/2.98*10^12
P = 0.053
Therefore the probability is 5.3%
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