Drawing Balls from a Bag

Data Science and AI Lecture Series

 

Problem Statement

A bag contains:

• 4 red balls
• 5 black balls
• 2 green balls

One ball is drawn at random. Find the probability that:

1. It is a red ball.
2. It is not black.
3. It is green or black.

Step 1: Total Balls in the Bag

Calculate the total number of balls in the bag:

\[
\text{Total balls} = \text{Red balls} + \text{Black balls} + \text{Green balls}
\]

\[
\text{Total balls} = 4 + 5 + 2 = 11
\]

The total number of balls in the bag is 11.

Step 2: Probability of Drawing a Red Ball

The probability of drawing a red ball is:

\[
P(\text{Red}) = \frac{\text{Number of red balls}}{\text{Total balls}}
\]

\[
P(\text{Red}) = \frac{4}{11}
\]

The probability of drawing a red ball is \(\frac{4}{11}\).

Step 3: Probability of Not Drawing a Black Ball

The number of balls that are not black is:

\[
\text{Not black balls} = \text{Red balls} + \text{Green balls}
\]

\[
\text{Not black balls} = 4 + 2 = 6
\]

The probability of not drawing a black ball is:

\[
P(\text{Not Black}) = \frac{\text{Number of not black balls}}{\text{Total balls}}
\]

\[
P(\text{Not Black}) = \frac{6}{11}
\]

The probability of not drawing a black ball is \(\frac{6}{11}\).

Step 4: Probability of Drawing a Green or Black Ball

The probability of drawing a green or black ball is:

\[
P(\text{Green or Black}) = P(\text{Green}) + P(\text{Black})
\]

Calculate each probability:

\[
P(\text{Green}) = \frac{\text{Number of green balls}}{\text{Total balls}} = \frac{2}{11}
\]

\[
P(\text{Black}) = \frac{\text{Number of black balls}}{\text{Total balls}} = \frac{5}{11}
\]

Add the probabilities:

\[
P(\text{Green or Black}) = \frac{2}{11} + \frac{5}{11} = \frac{7}{11}
\]

The probability of drawing a green or black ball is \(\frac{7}{11}\).

Final Results

Here are the probabilities for each scenario:

• Probability of drawing a red ball: \(\frac{4}{11}\)
• Probability of not drawing a black ball: \(\frac{6}{11}\)
• Probability of drawing a green or black ball: \(\frac{7}{11}\)

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Drawing Balls from a Bag

Video

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