Probability and Flower Color Relationship Reflection
Based on the data in this two-way table, which statement is true?
A. p(flower is yellow|flower is rose) ≠ p(flower is yellow)
B. p(flower is hibiscus|color is red) = p(flower is hibiscus)
C. p(flower is rose|color is red) = p(flower is red)
D. p(flower is hibiscus|color is pink) ≠ p(flower is hibiscus)
Final answer:
The notation p(A|B) represents the probability of event A given that event B has occurred. The notation p(A) refers to the unconditional or 'marginal' probability of event A. The difference between these probabilities would indicate that the color of a flower is not independent of its species.
Explanation: Without the specific values of the two-way table presented in the question, it is not possible for me to tell which statement A, B, C or D is exactly correct. However, I can certainly explain the concepts involved, hopefully allowing you to apply this to your specific table.
The notation p(A|B) denotes the probability of event A given that event B has occurred. So p(flower is yellow|flower is rose) is the probability that a flower is yellow given that the flower is a rose. It's calculated by dividing the number of yellow roses (both events A and B occurring) by the total number of roses (event B).
The notation p(A) refers to the unconditional or 'marginal' probability of event A. So p(flower is yellow) refers to the probability that a flower is yellow, without any given condition.
Therefore, if these probabilities were different, you could conclude that the color of the flower is not independent of its species, ie, the color distribution is different for different species of flowers.