Question

In a jar, there is a green, a blue, and a red marble. You draw (with replacement) a marble from the jar until you get the green marble. What is the probability that you draw exactly m times, where m is a positive integer?

Answer 1

Answer:

The value is $P( X = m ) = (\frac{2}{3} )^{m-1 } * \frac{1}{3}$

Step-by-step explanation:

From question we are told that

   The number of types of marbles present jar is n  =  3

Generally the probability of drawing a green marble is  

     $P(g) = \frac{1}{3}$

Generally the probability of drawing a marble that is not green is  

     $P(g') = 1 - \frac{1}{3} = \frac{2}{3}$

From the question we are told that there will be continuous drawing of marbles from the jar (in such a way that after each marble is drawn it is being replaced) until a green marble drawn

  Let m be the number of times marbles has been drawn when a green marble was gotten

it then means that for m - 1 times the marbles where drawn a green marble was not obtain.

Generally the probability drawing m times is mathematically is mathematically represented as

    $P( X = m ) = (P(g'))^{m-1 } * P(g)$

=>  $P( X = m ) = (\frac{2}{3} )^{m-1 } * \frac{1}{3}$