The likelihood of something happening is called the probability.
Terms related to probability:
Experiment : An activity which produces an outcome or result is called an experiment.
random Experiment : An Experiment in which exact outcome cannot be predicted in advance.
1) rolling a dice
2) Drawing a card from well-shuffled pack of playing cards
3) Tossing a coin
Trial : Performing an experiment is called a trial.
Event : Each possible outcomes of an experiment is called event.
Probability of an event : In a random experiment if 'n' is the total number of trials, then the empirical probability of the event E is P(E).
`"Number of trials happened in which event happened" / " Total number of trials"`
i.e. P(E) =`"Number of trials happened in which event happened" / n `
The Probability of an event lies between 0 and 1 (0 and 1 inclusive).
Shaalaa.com | Probability Experimental Approach
An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:-
|Vehicles per family|
|Less than 7000||10||160||25||0|
|7000 – 10000||0||305||27||2|
|10000 – 13000||1||535||29||1|
|13000 – 16000||2||469||59||25|
|16000 or more||1||579||82||88|
Suppose a family is chosen, find the probability that the family chosen is
(i) earning Rs 10000 − 13000 per month and owning exactly 2 vehicles.
(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than Rs 7000 per month and does not own any vehicle.
(iv) earning Rs 13000 − 16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.
Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg):- 4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00
Find the probability that any of these bags chosen at random contains more than 5 kg of flour.
A coin is tossed 1000 times with the following frequencies:
Head: 455, Tail: 545
Compute the probability for each event.
Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:
Two heads: 95 times
One tail: 290 times
No head: 115 times
Find the probability of occurrence of each of these events.
Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes:
|Outcome:||No head||One head||Two heads||Three heads|
If the three coins are simultaneously tossed again, compute the probability of:
(i) 2 heads coming up.
(ii) 3 heads coming up.
(iii) at least one head coming up.
(iv) getting more heads than tails.
(v) getting more tails than heads.