Solved Questions on Probability Distribution
Question 1: A box contains 4 blue balls and 3 green balls. Find the probability distribution of the number of green balls in a random draw of 3 balls.
Solution:
Given that the total number of balls is 7 out of which 3 have to be drawn at random. On drawing 3 balls the possibilities are all 3 are green, only 2 is green, only 1 is green, and no green. Hence X = 0, 1, 2, 3.
P(No ball is green) = P(X = 0) = 4C3/7C3 = 4/35
P(1 ball is green) = P(X = 1) = 3C1 × 4C2/7C3 = 18/35
P(2 balls are green) = P(X = 2) = 3C2 × 4C1/7C3 = 12/35
P(All 3 balls are green) = P(X = 3) = 3C3/7C3 = 1/35
Hence, the probability distribution for this problem is given as follows
X 0 1 2 3 P(X) 4/35 18/35 12/35 1/35
Question 2: From a lot of 10 bulbs containing 3 defective ones, 4 bulbs are drawn at random. If X is a random variable that denotes the number of defective bulbs. Find the probability distribution of X.
Solution:
Since, X denotes the number of defective bulbs and there is a maximum of 3 defective bulbs, hence X can take values 0, 1, 2, and 3. Since 4 bulbs are drawn at random, the possible combination of drawing 4 bulbs is given by 10C4.
P(Getting No defective bulb) = P (X = 0) = 7C4/10C4 = 1/6
P(Getting 1 Defective Bulb) = P (X = 1) = 3C1 × 7C3/10C4 = 1/2
P(Getting 2 defective Bulb) = P(X = 2) = 3C2 × 7C2/10C4 = 3/10
P(Getting 3 Defective Bulb) = P(X =3) = 3C3 × 7C1/10C4 = 1/30
Hence Probability Distribution Table is given as follows
X 0 1 2 3 P(X) 1/6 1/2 3/10 1/30
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Probability Distribution – Function, Formula, Table
A probability distribution is an idealized frequency distribution. In statistics, a frequency distribution represents the number of occurrences of different outcomes in a dataset. It shows how often each different value appears within a dataset.
Probability distribution represents an abstract representation of the frequency distribution. While a frequency distribution pertains to a particular sample or dataset, detailing how often each potential value of a variable appears within it, the occurrence of each value in the sample is dictated by its probability.
A probability distribution, not only shows the frequencies of different outcomes but also assigns probabilities to each outcome. These probabilities indicate the likelihood of each outcome occurring.
In this article, we will learn what is probability distribution, types of probability distribution, probability distribution function, and formulas.
Table of Content
- What is Probability Distribution?
- Probability Distribution Definition
- Random Variables
- Random Variable Definition
- Types of Random Variables in Probability Distribution
- Probability Distribution of a Random Variable
- Probability Distribution Formulas
- Expectation (Mean) and Variance of a Random Variable
- Expectation
- Variance
- Different Types of Probability Distributions
- Discrete Probability Distributions
- Bernoulli Trials and Binomial Distributions
- Binomial Distribution
- Cumulative Probability Distribution
- Probability Distribution Function
- Probability Distribution Table
- Prior Probability
- Posterior Probability
- Solved Questions on Probability Distribution