5. Petra has mastered the proofs for six of ten theorems. Two of the theorems will appear as questions on the final examination. What is the probability that a) neither of the proofs on the examination will be among those Petra mastered? b) at least one of the mastered proofs will appear on the examination?

Q: Assume the cards are drawn sequentially and without replacement. (permutations) In how many ways…

A: Given data, given that 5 Spades can be drawn from a standard deck of 52 cards. The cards are drawn…

Q: Consider a 9​-question test in which questions can be answered either correctly or incorrectly.…

A: Given that the test consists of total 9 questions.

Q: There are 9 numbers, 1, 2, 3... 9. Three numbers are randomly drawn. a) The three numbers are…

A:

Q: 5. How many 2-permutations are there of a set of eight objects?

A: We know that,  The formula pf permutations is,  nPr = P(n, r) = n!/(n-r)!

Q: Consider the tennis balls shown in the accompanying figure. Assume that one tennis ball is randomly…

A: Total number of balls = 6  Total number of orange balls = 3 odd number balls = { 1 , 3 , 5 }

Q: A lottery issues tickets whose number is made up of six digits, the first digit not being zero. What…

A: The lottery ticket consists of six digits.

Q: Let N be a three-digit positive integer with all different digits. What can we say about the…

A: Let N=ABC be any number then  N=100*A+10*B+C...........(1) Let reverse of N is CBA. Let N'=CBA now…

Q: 2. even numbers are in their natural positions. Determine the number of permutations of {1, 2, 3, 4,…

A: Here we use combination rules. And set theoretic rules.

Q: 4) If each digit can be used only once how many four-digit numbers can be formed from the digits…

A: We have given the following  numbers 0,3,2,5,4,6,8

Q: Three cards are taken from a randomly shuffled deck of 52 cards, one at a time without replacement.…

A: There are 52 cards in a deck of cards. In which, there are four different sorts of cards, namely,…

Q: Seven numbers are chosen at random from the whole numbers between 1 and 14​, ​inclusive, without…

A:

Q: Six numbers are chosen at random from the whole numbers between 1 and 17​, ​inclusive, without…

A: Six numbers are chosen at random from the whole numbers between 1 and 17, inclusive, without…

Q: Assume the cards are drawn sequentially and without replacement. In how many ways can 3 diamonds be…

A: Given information- We have given that 3 diamonds be drawn from a standard deck of 52 cards. The…

Q: An integer k ∈ {1,2,…,999,1000} is selected at random. What is the probability that: 1) k is…

A: It is given that k is an integer selected at random from the set of numbers 1, 2 ,…, 999, 1000. A…

Q: One 12-digit binary code (leading zeros allowed) is randomly generated by a computer. What is the…

A: a

Q: Three distinct numbers are chosen randomly from first 40 natural numbers.Find the probability that…

A:

Q: Select the correct choice that completes the sentences in parts (a) through (c). a) The probability…

A: We need to find the correct choice of option.

Q: a man has five different shirts, four different neckties, and three different sport jackets, howmany…

A: We have given information, Total number of shirts=5 Total number of neck ties=4 Total number of…

Q: On a quiz consisting of 3 true/false questions, an unprepared student must guess at each one. The…

A: The objective of this question is to understand the different possible outcomes when a student…

Q: Suppose I have 6 nieces and nephews (total, not six of each!) and I have just won a set of 8 CD's.…

A: a) To determine the number of different ways you can give each child a CD, we can use the concept of…