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Introduction to Probability - Use the probability scale to describe chance from impossible to certain

Grade 9CBSE

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

🔑Concepts

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Probability is a numerical measure of the likelihood that a specific event will occur, ranging from 00 to 11.

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The probability of an event EE, denoted as P(E)P(E), is always expressed as 0≤P(E)≤10 \le P(E) \le 1.

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Impossible Event: An event that can never happen has a probability of 00. Example: Rolling a 77 on a standard six-sided die.

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Certain Event: An event that is guaranteed to happen has a probability of 11. Example: Picking a red marble from a bag containing only red marbles.

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Even Chance: If an event is just as likely to happen as it is not to happen, its probability is 0.50.5 or 12\frac{1}{2}.

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Unlikely: Events with a probability between 00 and 0.50.5 are considered unlikely. The closer to 00, the less likely they are.

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Likely: Events with a probability between 0.50.5 and 11 are considered likely. The closer to 11, the more likely they are.

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The sum of the probabilities of all elementary events of an experiment is 11.

📐Formulae

P(E)=Number of outcomes favorable to ETotal number of possible outcomesP(E) = \frac{\text{Number of outcomes favorable to } E}{\text{Total number of possible outcomes}}

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 bag contains 55 white balls and 55 black balls. If one ball is drawn at random, what is the probability of drawing a white ball, and how would you describe this on the probability scale?

Solution:

Total outcomes = 5+5=105 + 5 = 10. Favorable outcomes (white balls) = 55. P(White)=510=0.5P(\text{White}) = \frac{5}{10} = 0.5

Explanation:

Since the probability is exactly 0.50.5, it is described as an Even Chance.

Problem 2:

In a deck of 5252 playing cards, what is the probability of drawing a card that is either Red or Black? Describe the chance.

Solution:

Total cards = 5252. Since every card in a standard deck is either Red or Black, the number of favorable outcomes is 5252. P(Red or Black)=5252=1P(\text{Red or Black}) = \frac{52}{52} = 1

Explanation:

A probability of 11 indicates that the event is a Certain Event.

Problem 3:

If the probability of it raining tomorrow is 0.20.2, how would you describe the chance of rain on the probability scale?

Solution:

P(Rain)=0.2P(\text{Rain}) = 0.2

Explanation:

Since 0.20.2 is greater than 00 but significantly less than 0.50.5, the event is described as Unlikely.