Question

Suppose a jar contains 12 red marbles and 27 blue marbles. If you reach in the jar and pull out 2 marbles at random at the same time, find the probability that both are red.

Answer 1

Answer:

9%

Step-by-step explanation:

The probability of picking one red marble among all of them is:

$P=\frac{12}{39}=0.31 \ (\ or \ 31 \%)$

However, the problem is asking for the probability of picking two red marbles. If we analyse, events are independent, so the probability should be the product of the probability of each red marble.

So, assuming that one red marble is picked at a time, after picking one, there would remain in the jar 11 red marbles and 38 as the total number of them. The probability would be:

$P=\frac{12}{39} \times \frac{11}{38}=\frac{132}{1482}=0.09 \ (or \ 9\%)$

So, there is a probability of 9% of picking two red marbles.

Answer 2

The probability picking two red marbles is 0.09

Recall :

Probability = required outcome / Total possible outcomes

Total possible outcomes = (12 + 27) = 39

Required outcome = number of red marbles = 12

First pick :

P(red marble) = $\frac{12}{39}$

Second marble :

Total marbles = 38 ; Red marbles = 12 - 1 = 11

P(red marble) = $\frac{11}{38}$

P(2 red marbles) = $\frac{12}{39} \times\frac{11}{38} = \frac{132}{1482}$

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