There are three boys and two girls. A committee of two is to be formed, find the probability of events that the committee contains:
a. at least one girl.
b. one boy and one girl.
c. only boys.
Solution:
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Since a committee of two is be formed
from three boys and two girls,
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Sample Space = { B1B2, B1B3, B1G1, B1G2,
B2B3, B2G1, B2G2, B3G1, B3G2, G1G2}
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a. Let A = Event of forming a committee
which contains atleast one girl
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A = { B1G1, B1G2, B2G1, B2G2, B3G1, B3G2,
G1G2}
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n(A) = 7
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b. Let B = Event that the committee
contains one boy and one girl.
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B = { B1G1, B1G2, B2G1, B2G2, B3G1, B3G2, }
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∴ n(B)
= 6
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P(B)
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=
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n(B)
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=
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6
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=
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3
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n(S)
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10
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5
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c. Let C = Event that the committee
contains only boys.
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C = { B1B2, B1B3, B2B3}
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∴ n(C)
= 3
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P(C)
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=
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n(C)
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=
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3
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=
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3
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n(S)
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10
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10
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