The probabilities are 0.25 and 0.454.
Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Given
A bucket contains 3 red balls, 4 yellow balls, and 5 purple balls.
The probability that the first ball is red and the second ball is purple.
We know the formula
[tex]\rm Probability = \dfrac{favorable\ events}{total\ events}[/tex]
For the first ball is red, then
Total event = 12
Favorable event = 3
[tex]\rm Probability = \dfrac{favorable\ events}{total\ events}\\\\\rm Probability = \dfrac{3}{12}\\\\\rm Probability = 0.25[/tex]
For the second ball is purple, then
one ball is taken from the bucket and is not replaced
Total event = 11
Favorable event = 5
[tex]\rm Probability = \dfrac{favorable\ events}{total\ events}\\\\\rm Probability = \dfrac{5}{11}\\\\\rm Probability = 0.454[/tex]
Thus the probabilities are 0.25 and 0.454.
More about the probability link is given below.
https://brainly.com/question/795909
