Question

A bag contains 5 red marbles, 4 green marbles and 1 blue marble. A marble is chosen at random from the bag and not replaced; then a second marble is chosen. What is the probability both marbles are green?

Answer 1

The Sensex is calculated using the 'freefloat market capitalisation' method. According to this method, the level of index at any point of time reflects the free-float market value of 30 component stocks relative to a base period. Initially, the index was calculated based on the 'full market capitalisation' method.

Answer 2

The correct answer is $\frac{2}{15}$.

Given: Number of red marbles = 5.

Number of green marbles = 4.

Number of blue marbles = 1.

To Find: The probability that both marbles are green.

Solution:

Probability = $\frac{Favorable outcome}{Total outcome}$

Total marbles = green + blue + red

Total marbles = 4+1+5 = 10

Probability that marble chosen is green P(G) = $\frac{Green marbles}{Total marbles}$

P(G) = $\frac{4}{10}=\frac{2}{5}$.

Now, if green ball is chosen without replacement.

Total balls = 10-1=9

Green balls = 4-1=3

P(G) = $\frac{Green marbles}{Total marbles}$

P(G) = $\frac{3}{9}$ = $\frac{1}{3}$

So, the probability both marbles are green = (Initial probability)(probability after choosing first marble without replacement)

=  $\frac{2}{5}*\frac{1}{3}=\frac{2}{15}$.

Hence, the probability both marbles are green is $\frac{2}{15}$.

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