The odds against Sam solving a Maths problem are 7:2, while the odds against Peter solving the same problem are 5:3. What are the odds in favour of Lisa solving the problem? (Note: All the three events are mutually exclusive of each other) A. 30/44 B. 30/43 C. 29/44 D. 29/43
Answers 1
Answer:
The odds in favour of Lisa solving the problem is 11:12
Step-by-step explanation:
Explanation:
Given, the odds against Sam solving a Maths problem are 7:2
The odds against Peter solving the problem are 5:3
Let the two events be [tex]E_{A}[/tex] and [tex]E_{B}[/tex]
Step1:
[tex]E_{A}[/tex] represent the event Sam solve the problem .
∴Probability that Sam solves the problem = P([tex]E_{A}[/tex]) = [tex]\frac{7}{9}[/tex]
Probability that Sam does not solve the problem =P( [tex]\bar{E_{A} }[/tex]) = 1- [tex]\frac{7}{9}[/tex]= [tex]\frac{2}{9}[/tex]
Step 2:
[tex]E_{B}[/tex] represent the event of Peter solving the problem
∴ Probability that Peter solve the problem = p([tex]E_{B}[/tex]) = [tex]\frac{5}{8}[/tex]
Now , probability that Peter dose not solve the problem = p([tex]\bar{E_{B} }[/tex]) = (1-[tex]\frac{5}{8}[/tex]) = [tex]\frac{3}{8}[/tex]
Step3:
Probability that Lisa solve the problem
= 1- (none of them solve the problem)
⇒P(E) = 1 - P([tex]\bar{E_{B} }[/tex]).P([tex]\bar{E_{A} }[/tex])
= 1 - [tex]\frac{3}{8}[/tex] × [tex]\frac{2}{9}[/tex] = 1- [tex]\frac{1}{12}[/tex] = [tex]\frac{11}{12}[/tex]
Final answer :
Hence , 11:12 are the odds in favour of Lisa solving the problem.
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