Question

It is $3:5$ against $A$ of solving a riddle and $2:5$ in favour of $B$ of solving the riddle. The probability that the riddle will not be solved is:

• A. $\frac{41}{56}$
• B. $\frac{15}{56}$
• C. $\frac{10}{56}$
• D. $\frac{11}{56}$

Answer 1

Answer: (B)

$\frac{15}{56}$

$3.5$ against $A$ solving a riddle $=\frac{3}{8}\times \frac{5}{8}$

$2.5$ Favour $B$ solving a riddle $=\frac{2}{7}\times \frac{5}{7}$

$\therefore$ Probability of riddle solved by $A=\frac{3}{8}\times \frac{5}{8}=\frac{6}{56}$

Probability of riddle solved by $B=\frac{5}{8}\times \frac{5}{7}=\frac{25}{56}$

Probability of riddle solved in favour of $B=\frac{2}{7}\times \frac{5}{8}=\frac{10}{56}$

$\Rightarrow$ Total probability $=\frac{6+25+10}{56}=\frac{41}{56}$

$\Rightarrow$ Probability that the riddle will not be solved $=1-\frac{41}{56}$

$=\frac{15}{56}$

Hence, the answer is $=\frac{15}{56}.$