Question

send me notes of probability​

Answer 1

Answer:

radhe radhe

Explanation:

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a ranydom event. The value is expressed between zero and one. It helps to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic theory which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment.

For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But if we toss two coins in the air, there could be three possibilities of events to occur, such as both the coins show heads or both shows tails or one shows heads and one tail, i.e.(H,H), (H,T),(T,T).aab

Answer 2

Probability Tricky Question

This questions are taken from [2]. One key to solve this question is write down the sample space and keep eliminating choices. Don’t conclude in hurry.

Q1 : A man comes up to you on the street and says: I have two children. At least one of them is a boy. What is the probability that the other child is also a boy?

Q2 : I have two kids, what are the odds I have 2 boys?

Q3 : A man comes up to you on the street and says: I have two children. The older one is a boy. What is the probability that the other child is also a boy?

Q4 : A man comes up to you on the street and says: I have two children. One is the boy standing here next to me. What is the probability that the other child is also a boy?

Q5 : Q. A man comes up to you on the street and says: I have two children. One of them is a boy who was born in the summer. What is the probability that the other child is also a boy? (There are four seasons : spring, summer, fall, winter)

Ans1 : (1/3)

Ans2 : (1/4)

Ans3 : (1/2)

Ans4 : (1/2)

Ans5 : (7/15)

Compare Q1 and Q5. Odd increases. Being born in summer is rare thing. If that rare thing has occurred there are higher chances of having two boys.

A bag contains (x) one rupee coins and (y) 50 paise coins. Four coins are taken from the bag and put away.

If a coin is now taken at random from the bag, what is the probability that it is a one rupee coin?

Ans is x/(x+y). It will remain same if we take either 1/2/3/4/5 coins because we don’t know which coin has been withdrawn. It is like trying out all possibilities and when we sum, it would come out as 1 only. [4]

The probability of a car passing a certain intersection in a 20 minute windows is 0.9. What is the probability of a car passing the intersection in a 5 minute window? (Assuming a constant probability throughout)

Ans : 0.4377 [5]

Independent Events

Mutually exclusive events means dependent event

For independent event = P(A/B) = P(A)

For mutually exclusive event if we know B has occurred, A will never occur.

independent event

If two random variables, X and Y, are independent, they satisfy the following conditions.

P(x|y) = P(x), for all values of X and Y.

P(X, Y) = P(x ∩ y) = P(x) * P(y), for all values of X and Y.

Here is an example from [6]. Ans is that X and Y are independent, A and B are not.