Question

Suppose that in fall quarter I had 70% freshman and 30% other in my classes, 50% of the students got B’s and 50% got something else, and 60% of the students that got a B were freshman. What percentage of the freshman got B’s? Show work.

Answer 1

Solution :-

Given data :

• Suppose that in fall quarter I had 70% freshman and 30% other in my classes,
• 50% of the students got B’s
• 50% got something else,
• 60% of the students that got a B were freshman.

Here we need to find out the percentage of the freshman got B’s.

Now consider as the class has "200 x" students.

Given as, 50% of the students got B’s.

Then, Number of students who got B's = 50% (200 x)

= 0.5 * 200 x

= 100 x

Number of students who got B's = 100 x

And given as, 60% of the students that got a B were freshman.

Then, Freshman ( who got B ) = 60% (100 x)

= 0.6 * 100 x

= 60 x

Freshman ( who got B ) = 60 x

And given as, 70% are freshman.

Then, Total Freshman = 70% (200 x)

= 0.7 * 200 x

= 140 x

Total Freshman = 140 x

Now, consider percentage of the freshman who got B’s.

i.e, Percentage of the freshman who got B’s = [Freshman ( who got B ) / Total Freshman ] * 100

= [ 60 / 140 ] * 100

= 0.4285 * 100

= 42.85 %

$\therefore$ Percentage of the freshman who got B’s = 42.85 % .