Question
Download Solution PDFThe problem of statistics is given in two sections of same standard. The odds against for section x to slove the problem are 4 ∶ 3 and odds in favour to section Y for solving the same problems are 7 ∶ 8. The probability that neither section solves the problem of statistics, if both sections try independent of each other, is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation
Problem of statistics is given in two sections of same standard
Odd against for section to solve the problem = 4 : 3
⇒ 4/4+ 3
⇒ 4/7
⇒ Odd in favour for section on y to solve problem = 7 : 8
⇒ 8/8 + 7
⇒ 8/15
But the probability that neither section solves the problems
If both the sections are independent of each other then not probability
P(X ∩ Y) = P(X).P(Y)
⇒ (4/7) × 8/15
⇒ 32/105
∴ The probability that neither section solves the problem of statistics if both sections by independent try independent of each other is 32/105.
Alternate Method Concept:
\({\rm{Odds\;in\;favour\;}} = \frac{\rm{Number\;of\;favourable\;outcomes}}{\rm{Number\;of\;unfavourable\;outcomes}}\;\)
\({\rm{Odds\;against\;}} = \frac{\rm{Number\;of\;unfavourable\;outcomes}}{\rm{Number\;of\;favourable\;outcomes}}\;\)
Calculation:
Given:
Odds against section X to solve the problem
\({\rm{Odds\;against\;}} = \frac{\rm{Number\;of\;unfavourable\;outcomes}}{\rm{Number\;of\;favourable\;outcomes}}=\frac{4}{3}\)
Probability of not solving:
\( \frac{\rm{Number\;of\;unfavourable\;outcomes}}{\rm{Number\;of\;favourable\;outcomes}\;+\;\rm{Number\;of\;unfavourable\;outcomes}}=\frac{4}{4+3}=\frac{4}{7}\)
Odds in favour of Y to solve a probelm:
\({\rm{Odds\;in\;favour\;}} = \frac{\rm{Number\;of\;favourable\;outcomes}}{\rm{Number\;of\;unfavourable\;outcomes}}\;\)
Problem of solving from Y will be
\( \frac{\rm{Number\;of\;favourable\;outcomes}}{\rm{Number\;of\;unfavourable\;outcomes}\;+\;\rm{Number\;of\;favourable\;outcomes}}=\frac{7}{7+8}=\frac{7}{15}\)
Problem of not solving by Y will be
\(1-\frac{7}{15}=\frac{8}{15}\)
The probability that neither section solves the problems will be
\(\frac{4}{7}\times \frac{8}{15}=\frac{32}{105}\)
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