A jar contains 3 blue marbles and 2 red marbles – In a jar containing 3 blue marbles and 2 red marbles, the concept of probability takes center stage. This exploration delves into the likelihood of drawing a blue marble, a red marble, or a specific marble from the jar, uncovering the fascinating world of chance and probability.
The total number of marbles in the jar is 5, with 3 being blue and 2 being red. These proportions lay the foundation for calculating the probabilities associated with various outcomes when drawing from the jar.
Probability in a Jar of Marbles
Probability is a mathematical concept that measures the likelihood of an event occurring. In this context, we will explore the probability of drawing marbles of different colors from a jar.
Overview
We have a jar containing 3 blue marbles and 2 red marbles, totaling 5 marbles.
Probability of Drawing a Blue Marble
The probability of drawing a blue marble is given by the formula:
P(Blue) = Number of blue marbles / Total number of marbles
In this case:
P(Blue) = 3 / 5 = 0.6
Probability of Drawing a Red Marble
Similarly, the probability of drawing a red marble is given by:
P(Red) = Number of red marbles / Total number of marbles
In this case:
P(Red) = 2 / 5 = 0.4
Probability of Drawing a Specific Marble
Conditional probability refers to the probability of an event occurring given that another event has already occurred. To calculate the probability of drawing a specific marble (e.g., the first blue marble), we use the following formula:
P(Specific) = P(Event)- P(Specific given Event)
In this case:
P(First Blue) = P(Blue) – P(First Blue given Blue)
P(First Blue) = 0.6 – (1 / 3) = 0.2
Probability of Drawing Multiple Marbles
When events are independent (i.e., the outcome of one event does not affect the outcome of the other), the probability of multiple events occurring is calculated as:
P(Multiple) = P(Event 1)- P(Event 2) – … – P(Event n)
For example, the probability of drawing a blue marble followed by a red marble is:
P(Blue and Red) = P(Blue) – P(Red) = 0.6 – 0.4 = 0.24
Probability Table, A jar contains 3 blue marbles and 2 red marbles
| Event | Probability | Explanation |
|---|---|---|
| Draw a blue marble | 0.6 | There are 3 blue marbles out of 5 total marbles. |
| Draw a red marble | 0.4 | There are 2 red marbles out of 5 total marbles. |
| Draw the first blue marble | 0.2 | There are 3 blue marbles and 1/3 chance of drawing the first blue one. |
| Draw a blue marble followed by a red marble | 0.24 | Independent events with probabilities 0.6 and 0.4, respectively. |
Probability Tree Diagram
Draw a blue marble(probability 0.6)
- Draw a red marble (probability 0.4)
- Draw a blue marble (probability 0.2)
Draw a red marble(probability 0.4)
- Draw a blue marble (probability 0.6)
- Draw a red marble (probability 0.4)
The tree diagram shows the different possible outcomes and their respective probabilities.
Question Bank: A Jar Contains 3 Blue Marbles And 2 Red Marbles
What is the probability of drawing a blue marble?
The probability of drawing a blue marble is 3/5 or 60%.
What is the probability of drawing a red marble?
The probability of drawing a red marble is 2/5 or 40%.
What is the probability of drawing a specific marble, such as the first blue marble?
The probability of drawing a specific marble is 1/5 or 20%.
