|Class 10 Maths Probability||Theoretical Approach|
In case of Empirical or Statistical or Experimental approach to Probability, we perform experiment & find the probability of occurrence of an event based on experimental data.
P(E) = Number of trials in which the event happened / Total number of trials
The requirement of repeating an experiment has some limitations, as it may be very expensive or unfeasible in many situations. E.g. Repeating the experiment of launching a satellite in order to compute the empirical probability of its failure during launching, or the repetition of the phenomenon of an earthquake to compute the empirical probability of a multistoried building getting destroyed in an earthquake. Also the results of the experimental approach are not consistent. Thus we use Classical Approach to Probability.
In classical approach we assume Probability of certain events. We know, in advance, that the coin can only land in one of two possible ways — either head up or tail up. We can reasonably assume that each outcome, head or tail, is as likely to occur as the other. We refer to this by saying that the outcomes head and tail, are equally likely.
Thus p(Head) = p(tail) = ½
For another example of equally likely outcomes, suppose we throw a die once. For us, a die will always mean a fair die. What are the possible outcomes? They are 1, 2, 3, 4, 5, 6. Each number has the same possibility of showing up. So the equally likely outcomes of throwing a die are 1, 2, 3, 4, 5 and 6.
Therefore p(1) = p(2) = p(3) = p(4) = p(5) = p(6) = 1/6
In this chapter we will assume that all the experiments have equally likely outcomes.
The theoretical probability (also called classical probability) of an event E, written as P(E), is defined as
P(E) = Number of outcomes favourable to E /Number of all possible outcomes of the experiment
where we assume that the outcomes of the experiment are equally likely.
Sum of the probabilities of all the elementary events of an experiment is 1
0 ≤ P(E) ≤ 1
Numerical: Find the probability of getting a head when a coin is tossed once. Also find the probability of getting a tail.
Solution: When you toss a coin, there are 2 possible equally likely outcomes: Head or Tail
P(Head) = Number of outcomes for Head/ Total number of outcomes
Or p(Head) = ½
Similarly p(tail) = ½
Note that p(head) + P(tail) = ½ + ½ = 1