Basic concept of Probability for class IX by GRAHMEDKVS
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Transcript of Basic concept of Probability for class IX by GRAHMEDKVS
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ProbabilityBy Mr.Golam
Robbani Ahmed
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What are the Chances?
A probability is something that can happen in more than one way.
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The outcomes of an experiment are the ways it can happen.
The event is the particular outcome we are looking for.
6 10 52
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?H HT TH T T H
The Probability of an Event P(Event) = the number of ways the event can happen the number of all possible outcomes
P(H+T) = 2 = 1 4 2
__ __
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BA
BAA
B14 12
35
2514
a) b)
P(red)
P(blue)
P(yellow or blue)1
5
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What is the probability of getting 4 fives?P(4 fives) =
4 52
CARD
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What is the probability of getting an even number?
213
DICE
P(even) =
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What is the probability of rolling two coins and getting H first and then T?
P(H & then T) =
COINS
14
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Random Experiment…
•…a random experiment is an action or process that leads to one of several possible outcomes. For example:
Experiment Outcomes
Tossing a coin Heads, Tails
Exam Marks Numbers: 0, 1, 2, ..., 100
Throwing a die 1,2,3,4,5,6
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Classical Approach…
•If an experiment has n possible outcomes [all equally likely to occur], this method would assign a probability of 1/n to each outcome.
•Experiment: Rolling a die•Sample Space: S = {1, 2, 3, 4, 5, 6}•Probabilities: Each sample point has a 1/6 chance of occurring.
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Classical Approach
•Experiment: Throwing two dies simultaneously•Sample Space: S = {2, 3, …, 12}•Probability Examples:•P(2) = 1/36
•P(7) = 6/36•P(10) = 3/36•
1 2 3 4 5 6
1 2 3 4 5 6 7
2 3 4 5 6 7 8
3 4 5 6 7 8 9
4 5 6 7 8 9 10
5 6 7 8 9 10 11
6 7 8 9 10 11 12
What are the underlying, unstated assumptions??
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Three coins are tossed. Find the probability of: 1. 3 heads 2. At least 2 heads. 3. At most 2 heads. At least 2 heads means minimum 2 heads i.e. 2 or more heads i.e. 3 .At most means maximum 2 heads i.e. up to 2 heads, i.e. less than or equal to 2 heads or no head.No. of favorable outs comes=(HHH),(HTH),(HTT),(THH),(THT),(TTT),(HHT)(TTH)=81.3 Head=3/82.At least 2 head=4/8=1/23.At most 2 head=7/8