Question

A pack of Original Starbursts contains four colors/flavors: red (cherry), orange (orange), yellow (lemon), and pink (strawberry). A recent survey asked people what their favorite Starburst color (or flavor) is. They asked 756 people and recorded their favorite color (or flavor) and their age group. The table below provides the results:
What is your favorite Original Starburst color (flavor)? Oran Red (C 81 69 75 225 Group e) Yellow (Lemon Pink (Stra 124 121 114 359 Total 254 252 250 756 ildren (6-12 years old) Teenagers (13- 19 years old) 25 32 28 85 24 30 ng Adults (20 - 26 years old) otal 87

What is the probability that a randomly selected survey respondent is a Teenager OR selects Pink (Strawberry) as their favorite Starburts color (flavor)?
0.1601
0.1735
0.3333
0.4749
0.6481
0.6548
0.6667

Based on all your calculations, the events "a randomly selected person is a Teenager" and 'a randomly selected person selects Pink (Strawberry) as their favorite Starburst color (flavor)" would be considered (check all that applies):
dependent events
independent events
mutually exclusive events
complementary events

You could determine if the events "a randomly selected person is a Teenager" and "a randomly selected person selects Pink (Strawberry) as their favorite Starburst color (flavor)" were independent by comparing the P(Pink | Teenager) with which of the following probabilities?
0.1601
0.4560
0.4749
0.4882
0.5000
0.6481
0.6667

Answer 1

Answer:

P ( P U T ) = 0.6481

Dependent events

P ( P / T ) = (359/756) = 0.4749

Step-by-step explanation:

Given:

- Pink : P

- Teenagers: T

Find:

- P( T u P )

- Are the events T and R dependent, independent, mutually exclusive, or complementary

- If the events are independent, then we can compare P ( P / T ).

Solution:

a)

For first part we will determine the total outcome for T and P:

                   Total outcomes P or T =  359 + 252 - 121 = 490

                                             (P U T) = (P) + (T) - (P n T)

The total number of possible outcomes are = 756

Hence, P ( P U T ) = 490 / 756 = 0.6481

b)

We are to investigate how the two events are related to one another:

- Check for dependent events:

              P ( T n P ) = P( T ) * P ( P / T )

              (121 / 756 ) = (252/756) * ( 121 / 252 )

              (121 / 756) = (121/756)  ....... Hence, events are dependent

- Check for independent events:

              P ( T n P ) = P( T ) * P ( P )

              (121 / 756 ) = (252/756) * ( 359 / 756 )

              (121 / 756) =/ (359/756)  ....... Hence, events are not independent

- Check for mutually exclusive events:

              P ( T U P ) = P( T )  + P ( P )

              (490 / 756 ) = (252/756) + ( 359 / 756 )

              (121 / 756) =/ (611/756)  ... Hence, events are not mutually exclusive

Hence, the two events are dependent on each other.

c)

If the events are said to be independent then the event:

               P ( P / T ) = P (P)

               P ( P / T ) = (359/756) = 0.4749