Probablities

• Wiskunde
• Middelbare school
• havo
• Leerjaar 1

Online lessons

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What's the percentage of yellow skittles in this picture?

What's the probability of rolling a 6 with one dice?

What's the probability of rolling 6 twice with two dice?

Probability?

Probability

• Probability is a measure of how likely something is to happen.

Probability

• Probability is a measure of how likely something is to happen.
• It is measured on a scale from 0 (when something is impossible) to 1 (when it is certain) or from 0% to 100%.

Probability

• Can you name something that is impossible (so something that never happens)?

Probability

• Can you name something that is impossible (so something that never happens)?
• And can you name something that is certain (so something that always happens)?

Probability

• Can you name something that is impossible (so something that never happens)?
• And can you name something that is certain (so something that always happens)?
• And can you name something that is evens chance (so 50% likely to happen)?

Impossible, evens chance or certain?

Are the following events impossible, evens chance or certain?

What's the probability of the Moon being larger than the Sun?

1. Impossible (0)
2. Evens chance (0.5)
3. Certain (1)
4. Something else

What's the probability of rolling a 7 with a 6-sided dice?

1. Impossible (0)
2. Evens chance (0.5)
3. Certain (1)
4. Something else

What's the probability of tossing heads with a coin?

1. Impossible (0)
2. Evens chance (0.5)
3. Certain (1)
4. Something else

What's the probability of getting wet when falling into a pool filled with water?

1. Impossible (0)
2. Evens chance (0.5)
3. Certain (1)
4. Something else

What's the probability of rolling a 2 with a 2-sided dice?

1. Impossible (0)
2. Evens chance (0.5)
3. Certain (1)
4. Something else

Events

• If the probability of an event happening is p, the probability of it not happening is 1 - p
• For example:
• If the probability of it raining today is 0.7 (or 70%) then the probability of it not raining today is 1 - 0.7 = 0.3 (so 30%).

The probability of event A happening is 0.3. What's the probability that event A does not happen?

1. 0.3
2. 1
3. 0.7
4. 0.97

Events

• We can also write it like this.

Events

• We can also write it like this.
• P(A) is the probability that event A happens.

Events

• We can also write it like this.
• P(A) is the probability that event A happens.
• So in the last example we had that P(A) = 0.3

Events

• We can also write it like this.
• P(A) is the probability that event A happens.
• So in the last example we had that P(A) = 0.3
• What is P(not A)?

Events

• We can also write it like this.
• P(A) is the probability that event A happens.
• So in the last example we had that P(A) = 0.3
• What is P(not A)?
• P(not A) = 1 - 0.3 = 0.7 

Events

• We can also write it like this.
• P(A) is the probability that event A happens.
• So in the last example we had that P(A) = 0.3
• What is P(not A)?
• P(not A) = 1 - 0.3 = 0.7
• Probability scale: 

Experiment

• The results of an experiment are known as outcomes. 
• In many situations, all the outcomes are equally likely.
• Can you name an experiment like this?

We have an experiment where we randomly choose a number between 1 and 10. What's the probability of choosing the number 8?

1. 0.8 (or 8 in 10)
2. 0.6 (or 6 in 10)
3. 0.1 (or 1 in 10)
4. 0

Events

• Any one outcome or combination of outcomes is known as an event. 

Events

• So say we have a fair dice, so the outcomes are equally likely
• What's the probability of rolling a 5?

Events

• So say we have a fair dice, so the outcomes are equally likely
• What's the probability of rolling a 5?

What's the probability of rolling a 6 with one dice?

Events

• What's the probability of rolling a 6 with one dice?

2 dice?

• Now what's the probability of rolling a 6 twice with two dice?
• We want to know the total number of possible outcomes.
• And also the number of ways the event can happen.

Probability of rolling a 6 twice with two dice

• How many possible outcomes?
• 1 and 1,  1 and 2,  1 and 3,  1 and 4,  1 and 5,  1 and 6,  2 and 1 ...

Probability of rolling a 6 twice with two dice

• How many possible outcomes?
• 1 and 1,  1 and 2,  1 and 3,  1 and 4,  1 and 5,  1 and 6,  2 and 1 ...

Probability of rolling a 6 twice with two dice

• The total number of possible outcomes is thus 6 x 6 = 36 

Probability of rolling a 6 twice with two dice

• In how many ways can you roll a 6 twice? 

Probability of rolling a 6 twice with two dice

• In how many ways can you roll a 6 twice? One time!

So, what's the probability of rolling 6 twice with two dice?

Events

• What's the probability of rolling a 6 twice with two dice?

Was this a fun lesson?

1. Yes
2. Absolutely
3. Definitely
4. ... Maybe

Homework

• On the Google Classroom there is a worksheet with exercises for this lesson.
• Make these exercises, take pictures of all of your answers and hand it in on the Google Classroom before the next lesson!
• Otherwise -> Huiswerk vergeten!