MATH SOLVE

3 months ago

Q:
# An urn is filled with marbles of various colors (but each marble only has one color). If the probability of pulling a red marble at random is 1/4 and the probability of pulling a blue marble at random is 1/3, what is the probability that a marble randomly pulled from the urn will be one of those two colors (red or blue)?

Accepted Solution

A:

Answer:[tex]\frac{7}{12}[/tex]Step-by-step explanation:We are given that The probability of pulling a red marble=[tex]\frac{1}{4}[/tex]The probability of pulling a blue marble=[tex]\frac{1}{3}[/tex]We have to find the probability that a marble at randomly pulled from the urn will be one of those two colors ( red or blue)When a marble is of red color then it can not be of blue color .When a marble is of blue color then it can not be of red color.[tex]P(Red\cap blue)=0[/tex]We know that [tex]P(A\cup B)=P(A)+P(B)-P(A\cap B)[/tex]A=Red marble B=Blue marble [tex]P(A)=\frac{1}{4}[/tex][tex]P(B)=\frac{1}{3}[/tex]Substitute the values then, we get [tex]P(Red\cup blue)=\frac{1}{4}+\frac{1}{3}=\frac{3+4}{12}=\frac{7}{12}[/tex]Hence, the probability of pulling red or blue marble from the urn=[tex]\frac{7}{12}[/tex]