23. A fair coin is flipped 8 times, and the sequence of eight results is ob- served. CHAPTER 3. COUNTING AND PROBABILITY a) How many outcomes are there in the sample space? b) What is the probability of each outcome? c) What is the probability of getting 3 heads and 5 tails? d) What is the probability of getting more tails than heads?

Q: Question 4: Simplify the following a. Vr3 а. b. Va²b4

A:

Q: Question 4 There is a committee made of five members. How many ways can they select a president, a…

A:

Q: 3. | rV3 – adr -

A: We have to find out solutions

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A: here given data, 20 blue and 18 black shock given, we need minimum sock that give guarantee of at…

Q: Can you please help with parts v & vi, thank you

A: (a) (V)   Obtain the probability of P(S and W)   The probability of P(S and W) is obtained below as…

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A:

Q: Question. The number of first-year students who were admitted and accepted for the 2022 fall…

A: Yes, we can assume independence, because sample size is less than 10% of the population.

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A: Group 1 would like to feed the bears, dolphins, and gorillas. Group 2 would like to feed the bears,…

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Q: Questions 37-40

A:

Q: Sec 7.5 1 A girl has 7 skirts, 10 blouses, and 4 pairs of shoes. How many different…

A: Count the options for each item: Skirts: There are 7 different skirts. Blouses: She has 10 different…

Q: If 2ª = 3b then =? O 1.4 O 1.5

A:

Q: 40 O 12 O 16 18 O 14 30 ?

A: Consider the figure given below :

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A: Here, we have to write negation of given sentence.

Q: 4. Evaluate: 46 = %3D

A: Given463

Q: Evaluate. 13!/12! A.6 B.26 C.12 D.13

A: Recall that, n!=n(n-1)!

Q: If (a-b)/c = (c-b)/a = 0.1, what are a, b, and c?

A: (a-b)/c = (c-b)/a = 0.1

Q: 10 assume that the number of production defects is 26 and that 12 of these are classified as major…

A: Given data, Number of production defects = 26 Number of major defects = 12 Number of design defects…

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.