Reviews of probability Question 1: Suppose we have a “ABCDE” litters how many words we can compose from them with 4 litters without repetition.

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Presentation transcript:

Reviews of probability Question 1: Suppose we have a “ABCDE” litters how many words we can compose from them with 4 litters without repetition.

Reviews of probability Question 2 In a class there are 25 boys and 12 girls, the teacher wants to select 1 boy and 1 girl to represent the class for a function. In how many ways can the teacher make this selection? Solution: Here the teacher is to perform two operations as: Selecting a boy from among the 25 boys and Selecting a girl from among the 12 girls. Then the teacher makes this selection by

Reviews of probability Question 3 In how many different ways can a true- false test consisting of 9 questions be answered?

Reviews of probability Answer: Each question has 2 choices True and False and they are 9 questions so the number of ways to answer the test is

Reviews of probability Question 4 In how many ways a committee consisting of 2 men and 1 woman, can be chosen from 5 men and 3 women? Solution: Out of 5 men there are 2 men can be chosen in 5C2 ways as:

Reviews of probability Solution: Out of 3 women there are 1 women can be chosen as 3C1 ways as: Then the committee can be chosen in

Reviews of probability Question 5 A die is loaded in such a way that an even number is twice as likely to occur as an odd number. If (E) is event that the number equal or less than 3 occurs in a single toss of the die.

Reviews of probability Answer 1. Find P(E) The sample space is Now we assign a probability of w to each odd number and a probability of 2w to each even number Then

Reviews of probability E= {1, 2,3} <= 3 P (E) = {w, 2w, w} Let A be the event that an even number turns up and let B be the event that a number divisive by 3 occurs. Find

Reviews of probability Solution: Event A is {2, 4, 6}, event B is {3, 6}.

Reviews of probability Example 6: Two dice are tossed; find the probability of getting an even number on the first die or a total number of 8. Solution: A: Getting an even number on the first die. B: The sum of the options obtained on the two dice 8.

Reviews of probability

Reviews of probability Example 7: EmployedUnemployedTotal Male Female Total If we select one person from above table and the event is M: a man is chosen. E: the once chosen is employed

Reviews of probability Solution: We can solve the above problem by two methods as: Directly from table as:

Reviews of probability Solution:2

Reviews of probability Example 8: In a fuse box containing 30 fuses of which 6 are defective. If 2 fuses are selected at random and removed from the box without replacing the first, what is the probability that both fuses are defective?

Reviews of probability Solution: Let A be the event that the first fuse is defective. Let B as the event that the A occurs and then the B occurs after A has occurred.

Reviews of probability Solution: