Answer to Question #129646 in Statistics and Probability for Nahashon Kimathi

Question #129646

A bag contains 10 marbles; 4 red and 6 black. A marble is chosen at random, the color noted and then replaced back to the bag. A second marble is then picked from the bag. What is the probability that?
a.Both marbles are red.
b.One of each color.

Expert's answer

a. The probability that 'the first marble is red' is "\\frac{4}{10}= \\frac{2}{5}."The probability to choose the second red marble is again "\\frac{4}{10}=\\frac{2}{5}" because we have returned the first one back. These events are independent so

"P(A) = \\frac{2}{5}*\\frac{2}{5}=\\frac{4}{25} =0.16"

b. The probability to choose a red marble is "\\frac{4}{10}= \\frac{2}{5}", the probability of choosing a black marble is "\\frac{6}{10}= \\frac{3}{5}." Events are independent, but we should take into account that we can choose the first black marble and the second red marble as well as the first red marble and the second black marble. Thus,

"P_1(B) = \\frac{2}{5}*\\frac{3}{5}=\\frac{6}{25} =0.24" (the first marble is red, the second marble is black);

"P_2(B) = \\frac{3}{5}*\\frac{2}{5}=\\frac{6}{25} =0.24" (the first marble is black, the second marble is red).

Total probability of choosing one marble of each color is "P(B)=P_1(B)+P_2(B)=0.48"