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Probability

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Calculating Probability

Probability and Statistics Calculating Probability

Courses Overview

🎬 Video Tutorial

(0:01) What is Probability?: Probability measures how likely an event is to happen, ranging from 0 (impossible) to 1 (certain), or from 0% to 100%.
(0:30) Basic Probability Calculation (Formula & Example): Probability of an event = (Number of favourable outcomes) / (Total number of outcomes). For example, if you randomly pick one ball from a set of 10, where 3 are red, the probability of drawing a red ball is 3 out of 10 (3/10), or 30%.
(1:39) What is Experimental Probability?: Experimental Probability is an estimated probability based on experiment results. For example, if you draw a ball 100 times and get 37 red balls, the experimental probability of picking red is 37%. This may differ from the true probability (40%), but with more trials, experimental probability gets closer to the true value.

📂 Revision Cards

Explanation of probability, including the likelihood of events happening and a scale ranging from impossible (0%) to certain (100%). — 1) Characteristic of Probability

Explaining probability of drawing a red ball from a bag of 10 balls (3 red, 7 blue) with a probability formula and example calculation. — 2) Calculating Probability (Formula & Example)

Drawing 100 times and getting 37 red and 63 blue. Explanation of experimental probability as estimated from outcomes compared to true probability. — 3) Experimental Probability

🍪 Quiz Time - Practice Now!

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Calculating Probability

1 / 6

Q: If you have a bag with 5 balls, 3 red and 2 blue, what is the probability of drawing a red ball?

$\frac{5}{10}$

$\frac{2}{5}$

$\frac{1}{2}$

$\frac{3}{5}$

Feedback: Not quite! There are 3 red balls out of 5 total balls. So, the probability of drawing a red ball is $\frac{3}{5}$ or 60%.

Feedback: Well done! There are 3 red balls out of 5 total balls. So, the probability of drawing a red ball is $\frac{3}{5}$ or 60%.

2 / 6

Q: A bag contains 12 balls, 3 red and 9 blue. What is the probability of drawing a blue ball?

$\frac{3}{9}$

$\frac{3}{4}$

$\frac{10}{12}$

$\frac{3}{12}$

Feedback: Not quite! There are 9 blue balls out of 12, so the probability of drawing a blue ball is $\frac{9}{12}$, which simplifies to $\frac{3}{4}$ or 75%.

Feedback: Well done! There are 9 blue balls out of 12, so the probability of drawing a blue ball is $\frac{9}{12}$, which simplifies to $\frac{3}{4}$ or 75%.

3 / 6

Q: A box contains 6 red marbles, 8 green marbles, and 10 blue marbles. What is the probability of drawing a green marble?

$\frac{1}{3}$

$\frac{1}{12}$

$\frac{1}{6}$

$\frac{1}{8}$

Feedback: Not quite! The total number of marbles is $6 + 8 + 10 = 24$. The probability of drawing a green marble is the number of green marbles ($8$) divided by the total number of marbles ($24$). So, the probability is $\frac{8}{24}$. This simplifies to $\frac{1}{3}$.

Feedback: Well done! The total number of marbles is $6 + 8 + 10 = 24$. The probability of drawing a green marble is the number of green marbles ($8$) divided by the total number of marbles ($24$). So, the probability is $\frac{8}{24}$. This simplifies to $\frac{1}{3}$.

4 / 6

Q: You roll a fair six-sided die. What is the probability of rolling a number greater than 4?

$\frac{5}{6}$

$\frac{1}{3}$

$\frac{1}{6}$

$\frac{3}{6}$

Feedback: Not quite! There are two numbers greater than 4 on a six-sided die: 5 and 6. Therefore, the probability is $\frac{2}{6}$, which simplifies to $\frac{1}{3}$.

Feedback: Well done! There are two numbers greater than 4 on a six-sided die: 5 and 6. Therefore, the probability is $\frac{2}{6}$, which simplifies to $\frac{1}{3}$.

5 / 6

Q: You draw a marble from a bag 500 times, and the results show 150 red marbles, 200 blue marbles, and 150 green marbles. What is the experimental probability of drawing a red marble?

$\frac{15}{30}$

$\frac{3}{10}$

$\frac{1}{3}$

$\frac{150}{200}$

Feedback: Not quite! The experimental probability of drawing a red marble is $\frac{150}{500}$ because there are 150 red marbles out of 500 total draws. To simplify, divide both the numerator (150) and denominator (500) by 50. This gives you $\frac{3}{10}$.

Feedback: Well done! The experimental probability of drawing a red marble is $\frac{150}{500}$ because there are 150 red marbles out of 500 total draws. To simplify, divide both the numerator (150) and denominator (500) by 50. This gives you $\frac{3}{10}$.

6 / 6

Q: If you flip a fair coin 10 times, does it guarantee that exactly half of the flips will be heads and half tails?

No, the result could be different.

Yes, it is guaranteed to be exactly half heads and half tails.

Feedback: Not quite! The outcome of flipping a fair coin 10 times is random, so there is no guarantee that exactly half of the flips will be heads and half tails. While it's likely to be close, other outcomes are possible.

Feedback: Well done! The outcome of flipping a fair coin 10 times is random, so there is no guarantee that exactly half of the flips will be heads and half tails. While it's likely to be close, other outcomes are possible.

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