A jar has 2 red marbles and 3 blue marbles. Two marbles are drawn at random without replacement from the jar. (a) Find the probability that the second marble is red. (b) Find the probability that the second marble is red, given that the first is blue

Answer:  The required answers are(a) 0.4.(b) 0.3.Step-by-step explanation:  Given that a jar has 2 red marbles and 3 blue marbles and two marbles are drawn at random without replacement from the jar.We are to find the probability that(a)  the second marble is red.(b)  the second marble is red, given that the first is blue.(a) Here, we need to find the probability that the second ball drawn is red. That is, the first ball may be red or blue.If first ball is red, then the probability that the second ball is red is given by[tex]p_1=\dfrac{2}{5}\times\dfrac{1}{4}=\dfrac{1}{10}.[/tex]If first ball is blue, then the probability that the second ball is red is given by[tex]p_2=\dfrac{3}{5}\times\dfrac{2}{4}=\dfrac{3}{10}.[/tex]Therefore, the probability that the second ball drawn is red is[tex]p=p_1+p_2=\dfrac{1}{10}+\dfrac{3}{10}=\dfrac{4}{10}=\dfrac{2}{5}=0.4.[/tex](b) Here, we need to find the probability that the second marble is red, given that the first is blue.From part (a), we get thatthe probability that the second ball is red, given that the first marble drawn is blue is[tex]p=\dfrac{3}{10}=0.3.[/tex]Thus, the required answers are(a) 0.4(b) 0.3.