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The Mathematics of Maybe: Introduction to Probability - What is Probability?

Grade 9CBSE

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

🔑Concepts

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Probability is the branch of mathematics that measures the degree of uncertainty of an event occurring. In Grade 9, we focus on Experimental or Empirical Probability.

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A Trial is an action that results in one or several outcomes. For example, tossing a coin or throwing a die is a trial.

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An Event is a collection of some outcomes of an experiment. It is usually denoted by capital letters like EE, AA, or BB.

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The Empirical Probability P(E)P(E) of an event EE is calculated based on the actual results of an experiment performed a finite number of times.

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The probability of any event always lies between 00 and 11 (inclusive), written as 0≤P(E)≤10 \le P(E) \le 1.

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An Impossible Event has a probability of 00, while a Certain Event has a probability of 11.

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The sum of probabilities of all possible outcomes in an experiment is always equal to 11.

📐Formulae

P(E)=Number of trials in which the event happenedTotal number of trialsP(E) = \frac{\text{Number of trials in which the event happened}}{\text{Total number of trials}}

0≤P(E)≤10 \le P(E) \le 1

∑P(Ei)=P(E1)+P(E2)+...+P(En)=1\sum P(E_i) = P(E_1) + P(E_2) + ... + P(E_n) = 1

💡Examples

Problem 1:

A coin is tossed 10001000 times with the following frequencies: Head: 455455, Tail: 545545. Compute the probability for each event.

Solution:

P(Head)=4551000=0.455P(\text{Head}) = \frac{455}{1000} = 0.455 P(Tail)=5451000=0.545P(\text{Tail}) = \frac{545}{1000} = 0.545

Explanation:

To find the empirical probability, we divide the frequency of the specific outcome by the total number of trials (10001000). Note that 0.455+0.545=10.455 + 0.545 = 1.

Problem 2:

A die is thrown 500500 times. The frequency of outcomes 1,2,3,4,5,1, 2, 3, 4, 5, and 66 are noted. If the number 33 appeared 7575 times, what is the probability of getting a 33?

Solution:

Let EE be the event of getting the number 33. P(E)=75500=320=0.15P(E) = \frac{75}{500} = \frac{3}{20} = 0.15

Explanation:

The probability is the ratio of the number of times 33 appeared (7575) to the total number of times the die was thrown (500500).

Problem 3:

In a survey of 200200 ladies, it was found that 142142 like coffee while 5858 dislike it. Find the probability that a lady chosen at random dislikes coffee.

Solution:

Total number of ladies =200= 200. Number of ladies who dislike coffee =58= 58. P(dislike)=58200=29100=0.29P(\text{dislike}) = \frac{58}{200} = \frac{29}{100} = 0.29

Explanation:

The total trials are represented by the total number of ladies surveyed. The event is 'disliking coffee', which occurred 5858 times.