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Probability Explained!

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💫 Short Summary

This math tutorial focuses on probability word problems, using the example of selecting marbles from a jar with different colors. It covers the probability of selecting specific colored marbles, both independently and in combination, and explains the concepts with clear calculations and concrete examples.

✨ Highlights
📊 Transcript
The probability of selecting a green marble from a jar containing 7 red, 6 green, 5 blue, and 2 yellow marbles is 30%.
00:00
Calculate the total number of marbles in the jar, which is 20.
Determine the probability of selecting a green marble by finding the number of green marbles (6) and dividing by the total number of marbles (20).
Simplify the fraction to 3/10, which is 0.3 as a decimal, or 30% probability.
The probability of selecting a green marble is 70%.
03:35
Calculate the number of marbles that are not green (7 + 5 + 2 = 14).
Determine the probability of not selecting a green marble by dividing the total non-green marbles by the total marbles (14/20).
Simplify the fraction to 7/10, which is 0.7 as a decimal, or 70% probability.
The probability of selecting a red marble and then a blue marble with replacement is 14.2%.
06:13
The probability of getting a red marble on the first try is 7/20.
The probability of getting a blue marble on the second try is 1/5, or 7/80 as a fraction.
Multiplying 7/20 by 7/80 gives the probability of getting a red marble and then a blue marble with replacement as 14.2%.
The probability of selecting a red marble and a blue marble without replacement is 9.21%.
09:29
The probability of getting a red marble on the first try is 7/20.
The probability of getting a blue marble on the second try without replacement, given that a red marble was selected on the first try, is 5/19.
Multiplying 7/20 by 5/19 gives the probability of selecting a red marble and a blue marble without replacement as 9.21%.
The probability of getting a red marble on the first try and then a blue marble on the second try without replacement is 7/24.
12:00
The probability of getting a red marble on the first try is 7/20.
The probability of getting a blue marble on the second try without replacement is 5/19.
The probability of getting a red marble on the first try and then a blue marble on the second try without replacement is 7/20 * 5/19 = 7/24.
The probability of getting a red and a blue marble without replacement is 18.4%.
14:07
The probability of not getting a red and a blue marble without replacement is 81.6%.
The method of finding the probability of an event not happening is subtracting the probability of the event happening from 100%.
The probability of selecting a red marble then a green marble or a blue marble then a yellow marble is 13%.
15:03
The probability of selecting a red marble then a green marble is 7/20 * 6/20 = 21/100.
The probability of selecting a blue marble then a yellow marble is 5/20 * 2/20 = 5/100.
Adding the two probabilities together gives 26/100, which simplifies to 13%.
💫 FAQs about This YouTube Video

1. What is the probability of selecting a green marble from the jar?

The probability of selecting a green marble from the jar, which contains 7 red marbles, 6 green marbles, 5 blue marbles, and 2 yellow marbles, is 30%.

2. How is the probability of not selecting a green marble calculated?

The probability of not selecting a green marble is 70%, and it can be calculated by finding the number of marbles that are not green and dividing by the total number of marbles in the jar.

3. What is the probability of selecting a red marble and then a blue marble with replacement?

The probability of selecting a red marble and then a blue marble with replacement is 14.2%.

4. What is the probability of selecting a red marble and a blue marble without replacement?

The probability of selecting a red marble and a blue marble without replacement is 9.21%.

5. What is the probability of getting a red marble on the first try and then a blue marble on the second try without replacement?

The probability of getting a red marble on the first try and then a blue marble on the second try without replacement is 7/24.

6. What is the probability of not getting a red and a blue marble without replacement?

The probability of not getting a red and a blue marble without replacement is 81.6%.

7. How is the probability of selecting a red marble then a green marble or a blue marble then a yellow marble calculated?

The probability of selecting a red marble then a green marble or a blue marble then a yellow marble is 13%.