Question 1194945
<font color=black size=3>
Part (a)


M = event of selecting a student in math
P(M) = probability of selecting a math student
P(M) = (number of math students)/(number total)
P(M) = 115/500
P(M) = 0.23


Answer: <font color = red>0.23</font>


===========================================================

Part (b)


E = event of selecting a student in English
P(E) = probability of selecting an English student
P(E) = (number of English students)/(number total)
P(E) = 205/500
P(E) = 0.41


Answer: <font color = red>0.41</font>


===========================================================

Part (c)


E and M = event of selecting student in both classes
P(E and M) = (number in both)/(number total)
P(E and M) = 45/500
P(E and M) = 0.09


Answer: <font color = red>0.09</font>


===========================================================

Part (d)


E or M = event of selecting a student in either class (or both)


n(E or M) = number of students in either class or both
n(E or M) = n(E) + n(M) - n(E and M)
n(E or M) = 205 + 115 - 45
n(E or M) = 275


P(E or M) = n(E or M)/(number total)
P(E or M) = 275/500
P(E or M) = 0.55


Answer: <font color = red>0.55</font>


===========================================================

Part (e)


n(E) = number in English class = 205
n(E and M) = number in both classes = 45


n(E not M) = number in English, but not math
n(E not M) = n(E) - n(E and M)
n(E not M) = 205 - 45
n(E not M) = 160


P(E not M) = n(E not M)/(500 total)
P(E not M) = 160/500
P(E not M) = 0.32


Answer: <font color = red>0.32</font>


===========================================================

Part (f)


I interpret this to mean "find the probability of someone that isn't in either class". Let me know if your teacher meant something else.


500 total students
n(E or M) = 275 in either class
n(not E and not M) = 500 - n(E or M)
n(not E and not M) = 500 - 275
n(not E and not M) = 225 students in neither class


225/500 = 0.45 is the probability of selecting a student that is not in English, and also not in Math either.


Answer: <font color = red>0.45</font>
</font>