# Probability Explained!

The Organic Chemistry Tutor2017-02-04

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730K views|7 years ago

💫 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%.

00:00Calculate 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%.

03:35Calculate 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%.

06:13The 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%.

09:29The 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.

12:00The 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%.

14:07The 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%.

15:03The 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%.

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