Probabilities

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WiskundeMiddelbare schoolhavoLeerjaar 3

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Probabilities

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\frac{​ 1 ​ ​}{​ 3 ​} \cdot \frac{​ 7 ​ ​}{​ 1 2 ​} =

\frac{​ 1 1 ​ ​}{​ 1 2 ​}

\frac{​ 8 ​ ​}{​ 1 5 ​}

\frac{​ 7 ​ ​}{​ 3 6 ​}

\frac{​ 1 1 ​ ​}{​ 1 4 4 ​}

Slide 2 - Quiz

What percentage corresponds to the fraction?

\frac{​ 1 ​ ​}{​ 5 ​}

20%

25%

Slide 3 - Quiz

What fraction corresponds to a probability of 0,4?

\frac{​ 2 ​ ​}{​ 5 ​}

\frac{​ 4 ​ ​}{​ 1 0 ​}

\frac{​ 1 ​ ​}{​ 4 0 ​}

\frac{​ 4 ​ ​}{​ 1 0 0 ​}

Slide 4 - Quiz

Today

Start (5 min)
New subject (15 min)
Bettermarks (20 min)
Exercise together (10 min)
Bettermarks (25 min)
End lesson (5 min)

Slide 5 - Slide

Note 14.2 Probabilities

The probability you roll 2 with a dice =

Notation: P(2) =

\frac{​ 1 ​ ​}{​ 6 ​}

\frac{​ 1 ​ ​}{​ 6 ​}

timer

2:00

Slide 6 - Slide

Probability trees

A basket contains 7 purple marbles and 3 yellow ones. Micha picks one marble from the basket and puts it back afterwards. Calculate the probability of picking two marbles of the same colour.

Slide 7 - Slide

Probability trees

A basket contains 7 purple marbles and 3 yellow ones. Micha picks one marble from the basket and puts it back afterwards. Calculate the probability of picking two marbles of the same colour.

Slide 8 - Slide

Probability trees

A basket contains 7 purple marbles and 3 yellow ones. Micha picks one marble from the basket and puts it back afterwards. Calculate the probability of picking two marbles of the same colour.

Slide 9 - Slide

Probability trees

A basket contains 7 purple marbles and 3 yellow ones. Micha picks one marble from the basket and puts it back afterwards. Calculate the probability of picking two marbles of the same colour.

Slide 10 - Slide

Probability trees

A basket contains 7 purple marbles and 3 yellow ones. Micha picks one marble from the basket and puts it back afterwards. Calculate the probability of picking two marbles of the same colour.

Slide 11 - Slide

Probability trees

A basket contains 7 purple marbles and 3 yellow ones. Micha picks one marble from the basket and puts it back afterwards. Calculate the probability of picking two marbles of the same colour.

Slide 12 - Slide

Probability trees

A basket contains 7 purple marbles and 3 yellow ones. Micha picks one marble from the basket and puts it back afterwards. Calculate the probability of picking two marbles of the same colour.

Slide 13 - Slide

Probability trees

A basket contains 7 purple marbles and 3 yellow ones. Micha picks one marble from the basket and puts it back afterwards. Calculate the probability of picking two marbles of the same colour.

P (G, G) = \frac{​ 3 ​ ​}{​ 1 0 ​} \cdot \frac{​ 3 ​ ​}{​ 1 0 ​} = \frac{​ 9 ​ ​}{​ 1 0 0 ​}

Slide 14 - Slide

Probability trees

A basket contains 7 purple marbles and 3 yellow ones. Micha picks one marble from the basket and puts it back afterwards. Calculate the probability of picking two marbles of the same colour.

P (G, G) = \frac{​ 3 ​ ​}{​ 1 0 ​} \cdot \frac{​ 3 ​ ​}{​ 1 0 ​} = \frac{​ 9 ​ ​}{​ 1 0 0 ​}

P (G, P) = \frac{​ 3 ​ ​}{​ 1 0 ​} \cdot \frac{​ 7 ​ ​}{​ 1 0 ​} = \frac{​ 2 1 ​ ​}{​ 1 0 0 ​}

Slide 15 - Slide

Probability trees

A basket contains 7 purple marbles and 3 yellow ones. Micha picks one marble from the basket and puts it back afterwards. Calculate the probability of picking two marbles of the same colour.

P (G, G) = \frac{​ 3 ​ ​}{​ 1 0 ​} \cdot \frac{​ 3 ​ ​}{​ 1 0 ​} = \frac{​ 9 ​ ​}{​ 1 0 0 ​}

P (G, P) = \frac{​ 3 ​ ​}{​ 1 0 ​} \cdot \frac{​ 7 ​ ​}{​ 1 0 ​} = \frac{​ 2 1 ​ ​}{​ 1 0 0 ​}

P (P, G) = \frac{​ 7 ​ ​}{​ 1 0 ​} \cdot \frac{​ 3 ​ ​}{​ 1 0 ​} = \frac{​ 2 1 ​ ​}{​ 1 0 0 ​}

P (P, P) = \frac{​ 7 ​ ​}{​ 1 0 ​} \cdot \frac{​ 7 ​ ​}{​ 1 0 ​} = \frac{​ 4 9 ​ ​}{​ 1 0 0 ​}

Slide 16 - Slide

Note 14.2: Probability trees

A basket contains 7 purple marbles and 3 yellow ones. Micha picks one marble from the basket and puts it back afterwards. Calculate the probability of picking two marbles of the same colour.

P (G, G) = \frac{​ 3 ​ ​}{​ 1 0 ​} \cdot \frac{​ 3 ​ ​}{​ 1 0 ​} = \frac{​ 9 ​ ​}{​ 1 0 0 ​}

P (G, P) = \frac{​ 3 ​ ​}{​ 1 0 ​} \cdot \frac{​ 7 ​ ​}{​ 1 0 ​} = \frac{​ 2 1 ​ ​}{​ 1 0 0 ​}

P (P, G) = \frac{​ 7 ​ ​}{​ 1 0 ​} \cdot \frac{​ 3 ​ ​}{​ 1 0 ​} = \frac{​ 2 1 ​ ​}{​ 1 0 0 ​}

P (P, P) = \frac{​ 7 ​ ​}{​ 1 0 ​} \cdot \frac{​ 7 ​ ​}{​ 1 0 ​} = \frac{​ 4 9 ​ ​}{​ 1 0 0 ​}

timer

5:00

Slide 17 - Slide

Note 14.2: Probability trees

The probability of picking the same coulour is:

P (G, G) = \frac{​ 3 ​ ​}{​ 1 0 ​} \cdot \frac{​ 3 ​ ​}{​ 1 0 ​} = \frac{​ 9 ​ ​}{​ 1 0 0 ​}

P (G, P) = \frac{​ 3 ​ ​}{​ 1 0 ​} \cdot \frac{​ 7 ​ ​}{​ 1 0 ​} = \frac{​ 2 1 ​ ​}{​ 1 0 0 ​}

P (P, G) = \frac{​ 7 ​ ​}{​ 1 0 ​} \cdot \frac{​ 3 ​ ​}{​ 1 0 ​} = \frac{​ 2 1 ​ ​}{​ 1 0 0 ​}

P (P, P) = \frac{​ 7 ​ ​}{​ 1 0 ​} \cdot \frac{​ 7 ​ ​}{​ 1 0 ​} = \frac{​ 4 9 ​ ​}{​ 1 0 0 ​}

P (G, G) + P (P, P) = \frac{​ 9 ​ ​}{​ 1 0 0 ​} + \frac{​ 4 9 ​ ​}{​ 1 0 0 ​} = \frac{​ 5 8 ​ ​}{​ 1 0 0 ​} = \frac{​ 2 9 ​ ​}{​ 5 0 ​}

Slide 18 - Slide

Bettermarks

Bettermarks 14.2 part 1
Until 10:45
Raise your finger if you have any questions
Finished? 14.2 part 2

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What is the percentage of blue markers?

Slide 23 - Slide

Bettermarks

Bettermarks 14.2 part 1 and 14.2 part 2
Until the end of the lesson
Raise your finger if you have any questions or if you're finished

Slide 24 - Slide

Probabilities

Items in this lesson

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Slide 2 - Quiz

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