Question

1. Among 100 students, a survey shows that 75 like M&Ms and 60 like Skittles, while 15 terrible people like neither. Let M be the event that a student likes M&Ms and S be the event that a student likes Skittles. (a) Express the event “a student likes M&Ms but does not like Skittles” as a mathematical phrase. (b) Express the event M ∩ S as a common language phrase. (c) Compute P(M ∩ S). (Hint: first determine P(M ∪ S) from the information given.)

Answer 1

a) Like M&M but doesn't like Skittles

So, mathematical phrase for this is: M - S or

Where S' is showing complement of set S.

b) implies 'a student likes M&Ms and Skittles both'

this symbol for intersection of two sets and this is used as 'and'.

c) n(M U S) = 100 - 15 = 85 (15 terrible doesn't include in any of the two sets)

n(M U S) = n(M) + n(S) - n(M S)

85 = 75 + 60 - n(M S)

n(M S) = 50

So, P(M S) =

Hence 0.5 is P(M S).