Question

The probability of passing in subject A,B,C,D are ¾, 2/3, 4/5 and ½ respectively. To qualify in the examination a student should pass in A and two subjects among three. What is the probability of qualifying in that examination.
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Answer 1

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Answer 2

Step-by-step explanation:

Given The probability of passing in subject A,B,C,D are ¾, 2/3, 4/5 and ½ respectively. To qualify in the examination a student should pass in A and two subjects among three. What is the probability of qualifying in that examination.

• Now the student passes in ABCD  passes in ABC fails in D (D bar) , passes in ABD fails in C (C bar) passes in ACD fails in B(B bar)
• So these will be the possible combinations in which he can qualify for the exam. So the probability is given by
• P of (ABCD U ABCD bar U ABC bar D U AB bar CD) = P(ABCD) + P(ABCD bar) + P(ABC bar D) + P (AB bar CD)
•                                                     = P(A) P(B)P(C)P(D) + P(A) P(B) P(C) P(D bar) + P(A) P(B) P(C bar) P(D) + P(A) P(B bar) P(C) P(D)
• Combining this we get and P(D) and P(D bar) = 1
•              
•    = So P(A) P(B) P(C) + P(A) P(B) P (C bar) P(D) + P(A) P(B bar) P(C) P(D)
•   = ¾ x 2/3 x 4/5 + ¾ x 2/3 x (1 – 4/5 ) x ½ + ¾ x (1 – 2/3) x 4/5 x ½  
•       = 2/5 + 1/20 + 1/10
•       = 8 + 1 + 2 / 20
•        = 11 / 20

Reference link will be

https://brainly.in/question/1215585