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A certain experiment has only A, B, and C as the possible outcomes. If
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25 Aug 2023, 03:02
25 Aug 2023, 03:02
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A certain experiment has only A, B, and C as the possible outcomes. If A and B are mutually exclusive events and P(A or B) = 0.7. If B and C are independent events and P (B and C) = 0.2, P(A) = ?
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1/30
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Re: A certain experiment has only A, B, and C as the possible outcomes. If
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25 Aug 2023, 22:42
25 Aug 2023, 22:42
1
P(A and B) = 0 (since A and B are mutually exclusive events )
P(A or B) =P(A)+P(B) =0.7 (since A and B are mutually exclusive events)
P(B and C)= P(B)*P(C) =0.2(since B and C are independent events)
P(A)+P(B)+P(C)=1
P(C)=1-(0.7)= 0.3
P(B)=2/3
P(A)= 7/10 -2/3 =1/30 =0.0333
P(A or B) =P(A)+P(B) =0.7 (since A and B are mutually exclusive events)
P(B and C)= P(B)*P(C) =0.2(since B and C are independent events)
P(A)+P(B)+P(C)=1
P(C)=1-(0.7)= 0.3
P(B)=2/3
P(A)= 7/10 -2/3 =1/30 =0.0333
Re: A certain experiment has only A, B, and C as the possible outcomes. If
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29 Aug 2023, 10:05
29 Aug 2023, 10:05
1
Answer : 1/30
Step-by-step explanation:
Since the experiment has only 3 events, therefore the sum of there probabilities should be 1.
P(A) + P(B) + P(C) = 1 ---------- Eq 1
Events A and B are mutually exclusive, therefore
P(A) + P(B) = 0.7 --------------- Eq 2
Events B and C are independent events, therefor
P(B) * P(C) = 0.2 ---------------- Eq 3
On substituting Eq 2 in Eq 1, we get
0.7 + P(C) = 1
P(C) = 0.3
Now replace the value of P(C) in Eq 3
P(B) * 0.3 = 0.2
P(B) = 2/3
Now replacing the value of P(B) in equation 2, we get
P(A) = 7/10 - 2/3
P(A) = 1/30 and that is the answer.
Step-by-step explanation:
Since the experiment has only 3 events, therefore the sum of there probabilities should be 1.
P(A) + P(B) + P(C) = 1 ---------- Eq 1
Events A and B are mutually exclusive, therefore
P(A) + P(B) = 0.7 --------------- Eq 2
Events B and C are independent events, therefor
P(B) * P(C) = 0.2 ---------------- Eq 3
On substituting Eq 2 in Eq 1, we get
0.7 + P(C) = 1
P(C) = 0.3
Now replace the value of P(C) in Eq 3
P(B) * 0.3 = 0.2
P(B) = 2/3
Now replacing the value of P(B) in equation 2, we get
P(A) = 7/10 - 2/3
P(A) = 1/30 and that is the answer.
