Question

Please show all steps and work please.

2. Given the following chart, find:

	A	B	C	D	F	Total
Senior	15	19	7	14	3	58
Junior	8	25	16	17	10	76
Sophomore	18	5	3	14	13	53
Freshmen	4	11	21	23	4	63
Total	45	60	47	68	30	250

A)   Find the probability that a student earned a “B” in the class.

       p(“B”) =

B)   Find the probability that a student earned a “C” given that they were a freshman.

       p(“C”|Freshman) =

C) Find the probability that a student was a Junior given that they earned a “F”.

    p(Junior|”F”) =

D) Find the probability that a student was a Senior.

     p(Senior) =

Answer 1

A) Total number of students are 250, and Total number of students who earned "B" is 60

Hence, $P(B)={60\over 250}=0.24$

B) There are 63 Freshmen, and out of these 21 Freshman have earned "C"

Therefore, $P(C\mid \text{Freshman} )={21\over 63}= {1\over 3}\approx 0.3333$

C) There are 30 students who earned "F" and out of these 10 were Junior students

Hence, $P( \text{Junior}\mid C )={10\over 30}= {1\over 3}\approx 0.3333$

D) Total number of students are 250, and Number of students who are Seniors is 58

Hence, $P( \text{Senior} )={58\over 250}= 0.232$