Probability Ques 50
Question-
Directions : The following paragraph shows the details of male and female students in five different groups. Consider the following paragraph and answer the questions given below :
There are 5 different groups $A$, $B, P, Q$ and $R$.
There are 9 males and 5 females in group $A$.
There are 5 males and 7 females in group B.
There are 7 males and 4 females in group $P$.
There are 4 males and 6 females in group $Q$.
There are 6 males and 3 females in group $R$.
Four students are selected from group $B$ one by one and not replaced. What is the probability that they are alternatively of different genders?
(1) $\frac{12}{85}$
(2) $\frac{14}{99}$
(3) $\frac{15}{79}$
(4) $\frac{13}{88}$
(5) $\frac{11}{71}$
Show Answer
Correct Answer: (2)
Solution: (2)
Look at the order $\Rightarrow$ first boy then girl or first girl, then boy Required probability $=\left(\left(\frac{5}{12}\right) \times\left(\frac{7}{11}\right) \times\left(\frac{4}{10}\right) \times\left(\frac{6}{9}\right)\right)+$
$\left(\left(\frac{7}{12}\right) \times\left(\frac{5}{11}\right) \times\left(\frac{6}{10}\right) \times\left(\frac{4}{9}\right)\right)$ $=\frac{7}{99}+\frac{7}{99}=\frac{14}{99}$
BETA
