Probability means measuring the uncertainty. In other words, probability means how likely an event is to occur.
For example: I toss a coin. There will be two events: Head and Tail i.e. either head will occur or tail will occur. Therefore, both the events will have half probability.
Probability concept includes some terms. Firstly, go through these terms, then i will start discussing the basic concept.
Some basic terms
Properties of Probability
- P(S) = `1` i.e. Probability of total number of outcomes (Sample Space) is `1`
- 0 `le` P(E)`le` 1 i.e. Probability of Sample space lies between `0` and `1`.its never less than zero.
- `barP(A) = 1- P(A)` i.e. Probability of not occurring of an event = 1- Probability of occurring an event.
- If in any question, "and' is used for events, then this means we have to multiply the probabilities if events are independent i.e. P(A and B) = P(A) `times` P(B)
- Similarly, if or is used then both the probabilities will be added i.e. P(A or B) = P(A) + P(B)
Solution: Total number of balls = `8 + 4= 12`
n(S)= number of ways of choosing `2` balls out of `12`= C`(12,2)`
`C(12,2) = (12!)/ (2! 10!)` = `66`
n(E)= number of ways of drawing same color balls i.e. either 2 out of 8 red balls OR 2 out of 4 blue balls
`n(E) = C(8,2) + C(4,2) = 34`
Probability = `34/66` = `17/33`
Example3: One card is drawn from a pack of `52` cards. Find the probability that
i) card drawn is black
ii) card drawn is a queen
iii) card drawn is black and queen
iv) card drawn is either black or queen
Solution: n(S)= `52`
i) n(E) = n(black) = `26`
P(black) = `26/52` = `1/2`
ii) n(E) = n(queen) = `4`
P(queen) = `4/52` = `1/13`
iii) n(black and queen) = `2` ( two queens are of black color)
P(black and queen)= `2/52` = `1/26`
iv) n(black or queen) = `26` (black cards including `2` queen) + `2` (rest two queens)= `28`
P(black or queen) = `28/52` = `7/13`