Question

The odds in favour of A solving a problem are 3 to 4 and the odds against B solving the same problem are 5 to 7. If they both try the problem, the probability that the problem is solved is:

• A. $\frac{41}{84}$
• B. $\frac{16}{21}$
• C. $\frac{5}{21}$
• D. $\frac{1}{4}$

Answer 1

The correct option is B $\frac{16}{21}$

$P\left(A\right)=\frac{3}{7},P\left(B\right)=\frac{7}{12}P\left(\overline{A}\right)=\frac{4}{7},P\left(\overline{B}\right)=\frac{5}{12}P(A\cup B)=1-P\left(\overline{A\cup B}\right)=1-P(\overline{A}\cap \overline{B})\therefore P(A\cup B)=1-\frac{4}{7}\times \frac{5}{12}=\frac{16}{21}$