Question

5. A survey of student pizza preferences showed that 43 students preferred cheese, 56 preferred sausage, 39 preferred pepperoni, 28 preferred supreme, 31 preferred another kind, and 19 did not like any type of pizza. Make your own probability distribution in order to answer the question. Match the probability of each outcome given to the correct outcome.

Answer 1

P (Cheese) = 0.199, P (Sausage) = 0.259, P (Pepperoni) = 0.181,

P (Supreme) = 0.130, P (Another Kind) = 0.144

and P (Does not like any kind) = 0.088

Explanation:

Given:

Number of students who prefer cheese = 43

Number of students who prefer sausage = 56

Number of students who prefer pepperoni = 39

Number of students who prefer supreme = 28

Number of students who prefer another kind = 31

Number of students who did not like any kind = 19

∴ The total number of students surveyed =
`43+56+39+28+31+19=216` The number of students who prefer pizza =
`43+56+39+28+31=197`

The probability that a students likes pizza is,

`P(Student\ likes\ pizza)=(No.\ of\ students\ who\ prefer\ pizza)/(Total\ no.\ of\ students\ surveyed)`

`=(197)/(216) \\=0.912`

The probability that a students does not likes pizza is,

`P(Student\ does\ not\ likes\ pizza)=(No.\ of\ students\ who\ does\ not\ prefer\ pizza)/(Total\ no.\ of\ students\ surveyed)`

`=(19)/(216) \\=0.088`

The probability distribution of students who prefer different kinds of pizza is:

• The probability that a student likes cheese:

`P(A\ Student\ prefers\ cheese)=(No.\ of\ students\ who\ prefer\ cheese)/(Total\ no.\ of\ students\ surveyed)`

`=(43)/(216)\\=0.199`

• The probability that a student likes sausage:

`P(A\ Student\ prefers\ sausage)=(No.\ of\ students\ who\ prefer\ sausage)/(Total\ no.\ of\ students\ surveyed)`

`=(56)/(216)\\=0.259`

• The probability that a student likes pepperoni:

`P(A\ Student\ prefers\ pepperoni)=(No.\ of\ students\ who\ prefer\ pepperoni)/(Total\ no.\ of\ students\ surveyed)`

`=(39)/(216)\\=0.181`

• The probability that a student likes supreme:

`P(A\ Student\ prefers\ supreme)=(No.\ of\ students\ who\ prefer\ supreme)/(Total\ no.\ of\ students\ surveyed)`

`=(28)/(216)\\=0.130`

• The probability that a student likes another kind:

`P(A\ Student\ prefers\ another\ kind)=(No.\ of\ students\ who\ prefer\ another\ kind)/(Total\ no.\ of\ students\ surveyed)`

`=(31)/(216)\\=0.144`

Thus, the probability distribution table is displayed below: