Question

1.  EXPLAIN THE CONCEPTS OF CONDITIONAL AND INDEPENDENT PROBABILITY AND GIVE EXAMPLES

Answer 1

Answer: The definitions and explanation are given below,

Explanation:

1. Conditional probability: The probability of one event is dependent on probability of second event, which already occurs is called conditional probability. The conditional probability of two events A and B is defined as $P(B|A)=\frac{P(A\cap B)}{P(A)}$ where event A is already occured.

For example: A urn contains 6 black and 7 white balls. Two balls are drawn from the bag. What is the probability of getting red ball after getting green ball.

Independent probability: The probability of one event is not dependent on probability of second event. The case of with replacement are the case of independent probability. If the  two events A and B are independent then $P(A\cap B)=P(A)P(B)$.

For example: A urn contains 2 black and 5 white balls.Two balls are drawn from the bag. First ball is drawn, after notice the color of ball we put it into the bag. What is the probability of getting red ball in second drawn.

2. Z-score: The formula for z-score is given below,

$Z=\frac{x-\mu}{\sigma}$

Where, x is observation, $\mu$ is population mean, $\sigma$ is population standard deviation. Z-score represents the relationship among population mean, population standard deviation and observations.

3. Confidence Interval: The confidence interval is the interval which shows the observations are true to the population parameter or not. Generally the the confidence interval is based on 95% confidence level.

The obervationsare lies outside the confidence interval, then there observations are not true to the population parameters. For 95% confidence level the 5% are known as error or level of significance.

4. Observational Study: Where each observation is included in the study is known as observational study like population senses.

Experiments: Where a small group of whole population is taken under studies and all observations are not included in the study is known as experiments. For example, samling.

The issues arise during data collection or interpretations are:

i) Irrelevant data provide by the persons

ii) Mistakes made by the person who is collecting the data.

iii) Target population is not clear.

iv) Aim of data collection is not clear.