Question

Size of college IITs Students Plan to Attend

	Small (Fewer than $5,000$ students)	Medium (From $5,000$ to $10,000$ students)	Large (More than $10,000$ students)	Total
IIT Bombay	$25$	$155$	$75$	$255$
IIT Roorkee	$39$	$112$	$98$	$249$
Total	$64$	$267$	$173$	$504$

Those planning to attend the college after graduation were chosen polled from the two high schools. The sizes of the colleges they planned to attend based on student body sizes were tabulated in the table above. Those $255$ from IIT Bombay had an average JEE score above $270$ and $249$ from IIT Roorkee had an average JEE score below $270$. What is the probability that the respondent would enroll at IIT Bombay if a poll respondent was chosen at random from those who are planning to attend a college with atleast $5000$ students.

• A. $\frac{210}{249}$
• B. $\frac{210}{440}$
• C. $\frac{230}{440}$
• D. $\frac{440}{504}$

Answer 1

Answer: (B)

$\frac{210}{440}$

From the Question,

$225$ from IIT Bombay $:$ JEE Score $<270$

$249$ from IIT Rooekee $:$ JEE Score $<270$

Polling from $2$ high schools

$P$(enroll at IIT Bombay)

$\Rightarrow$ No. of students more than $5000$ which includes medium and large $=155+75-25=210.$

Total no. of students in medium and large i.e above $5000$

$\Rightarrow$ Student from IIT Bombay and IIT Rooekee $=267+173=440.$

$\therefore P$(enroll at IIT Bombay) $=\frac{210}{440}.$

Hence, the answer is $\frac{210}{440}.$