 # 10th Class Chapter No 25 - Probablility in Maths for ICSE

#### Probability

The probability of an event denotes the likelihood of its happening. The probability of happening of an event E is denoted by P (E).

P (E) = </mo><mi>o</mi><mi>u</mi><mi>t</mi><mi>c</mi><mi>o</mi><mi>m</mi><mi>e</mi><mi>s</mi><mo stretchy="false"></mo><mspace width="thinmathspace" /><mi>f</mi><mspace width="thinmathspace" /><mi>a</mi><mi>v</mi><mi>o</mi><mi>u</mi><mi>r</mi><mi>a</mi><mi>b</mi><mi>l</mi><mi>e</mi><mspace width="thinmathspace" /><mi>t</mi><mi>o</mi><mspace width="thinmathspace" /><mi>E</mi></mrow><mrow><mi>T</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>l</mi><mspace width="thinmathspace" /><mi>n</mi><mi>u</mi><mi>m</mi><mi>b</mi><mi>e</mi><mi>r</mi><mspace width="thinmathspace" /><mi>o</mi><mi>f</mi><mspace width="thinmathspace" /><mi>a</mi><mi>l</mi><mi>l</mi><mspace width="thinmathspace" /><mi>p</mi><mi>o</mi><mi>s</mi><mi>s</mi><mi>i</mi><mi>b</mi><mi>l</mi><mi>e</mi><mspace width="thinmathspace" /><mi>o</mi><mi>u</mi><mi>t</mi><mi>c</mi><mi>o</mi><mi>m</mi><mi>e</mi><mi>s</mi></mrow></mfrac>[/itex]">Numberofevents(outcomes)favourabletoE/ Totalnumberofallpossibleoutcomes

#### Types of Probability

1. Empirical (or experimental) probability
When the probability is based on an actual experiment, it is called an empirical (or experimental) probability.
For example: A coin being tossed 100 times.

2. Classical (or theoretical) probability
When an experiment need not be performed for calculating the exact probability, the probability so obtained is called classical (or theoretical probability).
While calculating classical probability, we make certain assumptions and one of these assumptions is that all outcomes are equally likely.

#### Impossible event and sure event

• Probability of any event can never be less than 0 or more than 1. 0 p(E)  1
• If the probability of an event = 0; then the event is called an impossible event
• If the probability of an event = 1; then the event is called a certain or sure event
Posted in 10th on July 11 2020 at 07:29 AM

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