Suppose a jar contains 11 red marbles and 39 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.
.

Question

Suppose a jar contains 11 red marbles and 39 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. .

UpStudy AI · Accepted Answer

To find the probability that both marbles are red when 2 marbles are pulled out at random from the jar, we can use the concept of conditional probability.

Let's denote:
- $$ R $$ as the event that the first marble pulled out is red.
- $$ B $$ as the event that the second marble pulled out is red.

The probability of both marbles being red can be calculated using the formula for conditional probability:

$$ P(R \cap B) = P(R) \times P(B|R) $$

where:
- $$ P(R) $$ is the probability of the first marble being red.
- $$ P(B|R) $$ is the probability of the second marble being red given that the first marble is red.

Given:
- Total number of marbles in the jar = 11 red + 39 blue = 50 marbles.
- Probability of the first marble being red = $$ P(R) = \frac{11}{50} $$.

To find $$ P(B|R) $$, we need to consider the remaining marbles after the first red marble is pulled out. There are now 10 red marbles and 39 blue marbles left, making a total of 49 marbles.

Therefore, the probability of the second marble being red given that the first marble is red = $$ P(B|R) = \frac{10}{49} $$.

Now, we can calculate the probability that both marbles are red using the formula:

$$ P(R \cap B) = P(R) \times P(B|R) = \frac{11}{50} \times \frac{10}{49} $$

Let's calculate this probability.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\frac{11}{50}\times 10}{49}$$
- step1: Multiply the numbers:
  $$\frac{\frac{11}{5}}{49}$$
- step2: Multiply by the reciprocal:
  $$\frac{11}{5}\times \frac{1}{49}$$
- step3: Multiply the fractions:
  $$\frac{11}{5\times 49}$$
- step4: Multiply:
  $$\frac{11}{245}$$
The probability that both marbles are red when 2 marbles are pulled out at random from the jar is approximately 0.044898 or $$ \frac{11}{245} $$.
The probability that both marbles are red is approximately 0.0449 or $$ \frac{11}{245} $$.

Suppose a jar contains 11 red marbles and 39 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.
.

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