We appreciate your visit to A pack of Original Starbursts contains four colors flavors red cherry orange orange yellow lemon and pink strawberry A recent survey asked 756 people what. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
The probability that a randomly selected survey respondent is a Teenager OR selects Pink (Strawberry) as their favorite Starburst color (flavor) can be calculated by adding the individual probabilities of these two events occurring.
The probability of a respondent being a Teenager is 85/756, and the probability of selecting Pink (Strawberry) as their favorite flavor is 359/756. So, the probability of either event happening is (85/756) + (359/756) = 0.4749.
Based on these calculations, the events "a randomly selected person is a Teenager" and "a randomly selected person selects Pink (Strawberry) as their favorite Starburst color (flavor)" are NOT mutually exclusive events because they can both happen.
They are also NOT complementary events because they don't cover all possible outcomes.
Whether they are independent or dependent events can be determined by comparing P(Pink | Teenager) with the probability of Pink (Strawberry) regardless of age group, P(Pink).
If P(Pink | Teenager) is equal to P(Pink), they are independent events; otherwise, they are dependent.
In this case, P(Pink | Teenager) is 114/85, and P(Pink) is 359/756. Comparing these probabilities, we find that P(Pink | Teenager) is not equal to P(Pink), so the events are dependent.
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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
