A bucket contains 3 red balls, 4 yellow balls, and 5 purple balls. one ball is taken from the bucket and is not replaced. another ball is taken from the bucket. what is the probability that the first ball is red and the second ball is purple?

The probabilities are 0.25 and 0.454.ProbabilityProbability 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.To find The probability that the first ball is red and the second ball is purple.How to find 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, thenTotal event = 12Favorable 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, thenone ball is taken from the bucket and is not replacedTotal event = 11Favorable 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.