Probability From a Bag of Objects

Probability from a bag of objects

When a problem asks for the probability of drawing an object from a bag, use the basic idea:

Probability = favorable outcomes / total possible outcomes

1) Count carefully

• Find the total number of objects in the bag.
• Find how many objects match the event you want: a color, type, number, or condition.
• If the bag changes after a draw, pay attention to whether the problem says with replacement or without replacement.

2) Write the probability as a fraction

Put the number of favorable objects over the total number of objects. If there is more than one step, multiply probabilities for consecutive draws when appropriate.

3) Simplify the final answer

Reduce the fraction to lowest terms. If the answer is a decimal or percent, convert only if the question asks for it.

4) Check your work

• The numerator should never be larger than the denominator.
• A probability must be between 0 and 1.
• If the event is impossible, the probability is 0; if it is certain, the probability is 1.

Example method

If a bag has 5 red objects and 3 blue objects, then the probability of drawing red is (5/8). This is already simplified.

Use the same steps for every bag problem: count, form the fraction, simplify, and check.