Question

A problem in mathematics is given to four students A, B, C and D. Their chances of solving the problem are 1/2, 1/3, 1/4 and 1/5 respectively. What is the probability that the problem will be solved?

Answer 1

Step-by-step explanation:

Given A problem in mathematics is given to four students A, B, C and D. Their chances of solving the problem are 1/2, 1/3, 1/4 and 1/5 respectively. What is the probability that the problem will be solved?

• According to the question:
• Probability that A solves the problem will be  
• P (A) = 1/2  
• Probability that B solves the problem will be
• P (B) = 1/3  
• Probability that C solves the problem will be
• P (C) = 1/4  
• Probability that D solves the problem will be
• P (D) = 1/5  
• Let P (E ) be the probability that the problem is solved.
• Now P (E’) be probability that problem is not solved by either A,B,C or D will be.
• P (E’) = P(A’) x P(B’) x P(C’) x P(D’)
• P (E’) =  1/2 x 1/3 x 1/4 x 1/5 = 1/120
• Therefore P(E ) = 1 – P(E’)
•                         = 1 – 1/120
• So P(E ) = 119 / 120

Therefore probability that problem is solved is 119 / 120

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