There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the b

Discussion in 'Calculator Requests' started by math_celebrity, Nov 27, 2018.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    There is a bag filled with 5 blue, 6 red and 2 green marbles. A marble is taken at random from the bag, the colour is noted and then it is replaced. Another marble is taken at random. What is the probability of getting exactly 1 blue?

    Find the total number of marbles in the bag:
    Total marbles = 5 blue + 6 red + 2 green
    Total marbles = 13

    The problem asks for exactly one blue in 2 draws with replacement. Which means you could draw as follows:
    Blue, Not Blue
    Not Blue, Blue

    The probability of drawing a blue is 5/13, since we replace the marbles in the bag each time.
    The probability of not drawing a blue is (6 + 2)/13 = 8/13

    And since each of the 2 draws are independent of each other, we multiply the probability of each draw:
    Blue, Not Blue = 5/13 * 8/13 =40/169
    Not Blue, Blue = 8/13 * 5/13 = 40/169

    We add both probabilities since they both count under our scenario:
    40/169 + 40/169 = 80/169

    Checking our fraction simplification calculator, we see you cannot simplify this fraction anymore.
    So our probability stated in terms of a fraction is 80/169
    Stated in terms of a decimal, it's 0.4734
     

Share This Page