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  • The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the student has <img alt="75 \%" src="https://entrancecorner.oncodecogs

The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p and c respectively. Of these subjects, the student has 75 \% chance of passing in at least one, a 50 \%  chance of passing in at least two and a 40 \% chance of passing in exactly two. Following relations are drawn in \mathrm{m}, \mathrm{p}, \mathrm{c}
\mathrm{I.\: \: \: p+m+c=\frac{27}{20} \: \: \: \: II.\: \: \: p+m+c=\frac{13}{20}}
\mathrm{III. \: \: (\mathrm{p}) \times(\mathrm{m}) \times(\mathrm{c})=\frac{1}{10}}

Option: 1

Only relation I is true


Option: 2

Only relation ill is true.


Option: 3

Relations II and III are true


Option: 4

Relations I and III are true.


Answers (1)

best_answer


\mathrm{Given, \alpha+\beta+\gamma+d+e+f+g=\frac{75}{100}}\quad \ldots(1)
\mathrm{\& \quad d+e+f+g=\frac{50}{100}}\quad \ldots(2)
\mathrm{\& \quad d+e+f=\frac{40}{100}}\quad \ldots(3)

Subtracting (2) & (3) \mathrm{g=\frac{10}{100}=10 \%} &  subtracting (1) & (2),

\mathrm{\alpha+\beta+\gamma=\frac{25}{100}}

\mathrm{So \: M \times P \times C h=10 \%}
\mathrm{Now, M+P+C h}

\mathrm{=(\alpha+d+g+f)+(\beta+d+e+g)+(\gamma+e+f+g) \\ }
\mathrm{=(\alpha+\beta+\gamma)+2(d+e+f)+3 g }
\mathrm{=\frac{25}{100}+2\left(\frac{40}{100}\right)+3\left(\frac{10}{100}\right) }
\mathrm{=\frac{135}{100}=\frac{27}{20} }
 

Posted by

rishi.raj

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