Probability Ques 29
Question-
There are 3 people A, B and C. Probability that A speaks truth is $\frac{3}{10}$, probability that B speaks truth is $\frac{3}{7}$ and probability that C speaks truth is $\frac{5}{6}$. For a particular kind of question asked, at most 2 people speak truth. All people answer to a particular question asked. What is the probability that B will speak truth for a particular question asked ?
(1) $\frac{8}{19}$
(2) $\frac{9}{28}$
(3) $\frac{5}{23}$
(4) $\frac{11}{31}$
(5) $\frac{7}{20}$
(IBPS Bank PO/MT CWE (Main Exam) 18.11.2018)
Show Answer
Correct Answer: (2)
Solution: (2)
B speaks truth at any case. So, now at most 2 people speak truth for 1 question.
Case 1 : B and A speak truth
Probability $=\frac{3}{7} \times \frac{7}{10} \times \frac{5}{6}=\frac{5}{20}$
Case 2 : B and C speak truth
Probability $=\left(\frac{3}{7}\right) \times\left(\frac{1-3}{10}\right) \times\left(\frac{5}{6}\right)$ $=\frac{3}{7} \times \frac{7}{10} \times \frac{5}{6}=\frac{5}{20}$
Case 3 : Only B speaks truth
Probability $=\left(\frac{3}{7}\right) \times\left(\frac{1-3}{10}\right) \times\left(\frac{1-5}{6}\right)$ $=\frac{3}{7} \times \frac{7}{10} \times \frac{1}{6}=\frac{1}{20}$
Add the three cases $=\left(\frac{6}{20}\right)+\left(\frac{3}{140}\right)=\frac{45}{140}=\frac{9}{28}$
BETA
