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Data Handling - Probability Outcomes

Grade 6IB

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Probability is a measure of the likelihood that a particular event will occur. It is expressed as a value between 00 and 11.

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An Experiment is an action or process (like tossing a coin or rolling a die) that has a set of possible results called outcomes.

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The Sample Space is the set of all possible outcomes of an experiment. For example, the sample space for rolling a die is S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\}.

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An Event is a specific outcome or a collection of outcomes that we are interested in.

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The Probability Scale ranges from 00 (Impossible event) to 11 (Certain event). A probability of 0.50.5 (or 12\frac{1}{2}) means an event is 'Even Chance' or equally likely to happen as not.

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Theoretical Probability is calculated based on the assumption that all outcomes in the sample space are equally likely.

📐Formulae

P(E)=Number of favorable outcomesTotal number of possible outcomes in the sample spaceP(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes in the sample space}}

0≤P(E)≤10 \le P(E) \le 1

P(E)+P(not E)=1P(E) + P(\text{not } E) = 1

💡Examples

Problem 1:

A fair six-sided die is rolled once. What is the probability of rolling an even number?

Solution:

P(Even)=36=12P(\text{Even}) = \frac{3}{6} = \frac{1}{2}

Explanation:

The sample space of a six-sided die is S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\}, so the total number of outcomes is 66. The even numbers in this set are {2,4,6}\{2, 4, 6\}, which gives 33 favorable outcomes. Using the formula P(E)=favorabletotalP(E) = \frac{\text{favorable}}{\text{total}}, we get 36\frac{3}{6}, which simplifies to 12\frac{1}{2} or 0.50.5.

Problem 2:

A bag contains 55 red marbles, 33 blue marbles, and 22 yellow marbles. If one marble is picked at random, what is the probability that it is NOT red?

Solution:

P(Not Red)=3+25+3+2=510=12P(\text{Not Red}) = \frac{3 + 2}{5 + 3 + 2} = \frac{5}{10} = \frac{1}{2}

Explanation:

First, find the total number of marbles: 5+3+2=105 + 3 + 2 = 10. The outcomes that are 'not red' are blue or yellow. Number of blue and yellow marbles =3+2=5= 3 + 2 = 5. Thus, the probability is 510\frac{5}{10}, which simplifies to 12\frac{1}{2}.

Problem 3:

If the probability of it raining tomorrow is 0.250.25, what is the probability that it will not rain?

Solution:

P(No Rain)=1−0.25=0.75P(\text{No Rain}) = 1 - 0.25 = 0.75

Explanation:

Since the sum of the probability of an event happening and not happening is always 11, we subtract the given probability from 11: 1−0.25=0.751 - 0.25 = 0.75.