Question

Suppose an opaque jar contains 7 red marbles and 10 green marbles. The following exercise refers to the experiment of picking two marbles from the jar without replacing the first one. What is the probability of getting a green marble and a red marble? (Enter your probability as a fraction. Hint: How is this exercise different from finding the probability of getting a green marble first and a red marble second?)

Answer 1

We know :

Probability = Favorable outcome / Total outcomes

Total marbles = 17

Red marbles = 7

Green marbles = 10

Probability of getting a green marble and a red marble =

Probability of getting a green marble first and a red marble second + Probability of getting a red marble first and a green marble second

Now,

When we get first marble , there are 17 marble present

When we get second marble , there are 16 marble present

So,

Probability of getting a green marble first and a red marble second = ( 10 / 17 ) * ( 7 / 16 ) = 35 / 136

Probability of getting a red marble first and a green marble second = ( 7 / 17 ) * ( 10 / 16 ) = 35 / 136

Probability of getting a green marble and a red marble = 35 / 136 + 35 / 136 = 35 / 68