There is a jar of jelly beans with the following flavors: 12 are grape, 17 are blueberry, 5 are pineapple and 13 are coconut. What is the probability, expressed as a percent, of selecting either a grape or blueberry replacing it and then a coconut or pineapple?
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The probability of selecting either a grape or blueberry, replacing it and then coconut or pineapple is 24%.
-----------------------------------EXPLANATION-------------------------------------
First, we look at what probability is.
PROBABILITY
Probability is a numerical description of how likely an event is to occur. It is about the chances of a certain event happen.
Back to your problem above, the problem is asking for the chances of selecting either a grape or blueberry, replacing it and then coconut or pineapple.
To find the probability of the events, we have the formula, the number of events to happen over the total number of possible outcomes.
Probability = number of events to happen / total number of the possible outcomes
There are two cases in the problem, which are:
-Probability of selecting either a grape or blueberry.
-Probability of selecting a coconut or pineapple.
We need to find the probability of each case first, for us to come up with the probability of the two cases to happen.
Problem 1: Probability of selecting either a grape or blueberry.
We have two possible events to happen.
1. Probability of Selecting a Grape = 12⁄47
The number of events to happen - 12
The total number of possible outcomes - 47
2. Probability of Selecting a Blueberry = 17⁄47
The number of events to happen - 17
The total number of possible outcomes - 47
Now, to find out if one event or another could happen, we need to add the probabilities.
12⁄47 + 17⁄47 = 29⁄47 = 0.62 = 62%
The probability of selecting either a grape or blueberry is 62%.
Problem 2: Probability of selecting a coconut or pineapple.
We have two possible events to happen.
1. Probability of Selecting a Coconut = 13⁄47
The number of events to happen - 13
The total number of possible outcomes - 47
2. Probability of Selecting a Pineapple = 5⁄47
The number of events to happen - 5
The total number of possible outcomes - 47
We also need to add to find out if one event or another could happen.
13⁄47 + 5⁄47 = 18⁄47 = 0.38 = 38%
Now, to find the probability of both cases happening, we need to multiply their probabilities.
62% × 38% = 0.62 × 0.38 = 0.24 = 24%
Final Answer:
The probability of selecting either a grape or blueberry replacing it and then coconut or pineapple is 23.56%.
I hope this helps. ^^
For more information on probability, visit these websites:
https://mathisfun.com
https://revisionmaths.com/gcse-maths-revision/statistics-handling-data/probability
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