Answer:
Step-by-step explanation:
For question 1, the result is calculated by dividing the percentage of students in the sports club by the SAT average, while for question 2, the answer is no since the definitions yield contrary outcomes.
There are several possible outcomes. The initial composition of the urns is as follows: Urn 1 contains 2 red chips and 4 white chips, totaling 6 chips, whereas Urn 2 has 3 red and 1 white, amounting to 4 chips. When a chip is drawn from the first urn, the probabilities are as follows: for a red chip, it is probability is (2 red from 6 chips = 2/6 = 1/2); for a white chip, it is (4 white from 6 chips = 4/6 = 2/3). After the chip is transferred to the second urn, two scenarios can arise: if the chip drawn from the first urn is white, then Urn 2 will contain 3 red and 2 white chips, making a total of 5 chips, creating a 40% chance for drawing a white chip. Conversely, if a red chip is drawn first, Urn 2 will contain 4 red and 1 white chip, which results in a 20% chance of drawing a white chip. This scenario exemplifies a dependent event, as the outcome hinges on the type of chip drawn first from Urn 1. For the first scenario, the combined probability is (the probability of drawing a white chip from Urn 1) multiplied by (the probability of drawing a white chip from Urn 2), equaling 26.66%. For the second scenario, the probabilities yield a value of 6%.
Calculate the probability of each pen color by dividing the number of times each color was chosen by the total selections:
Red pens: 6 out of 30, which simplifies to 1/5
Blue pens: 10 out of 30, which simplifies to 1/3
Black pens: 14 out of 30, which simplifies to 7/15
To find the likelihood of first selecting a blue pen and then a red pen, multiply their individual probabilities:
(1/3) × (1/5) = 1/15
The resulting probability is 1/15.
