5. Petra has mastered the proofs for six of ten theorems. Two of the theoremswill appear as questions on the final examination. What is the probability thata) 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?C11

Answered: Image /qna-images/answer/6a889d93-489b-4ab4-8947-294566f817bd.jpg

Answered: 5. Petra has mastered the proofs for…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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13. Determine the number of permutations of (1,2,...,9} in which at least one odd integer is in its natural position.
Two dices are thrown. What is the probability that a)we'll get the same number twice b)the number in the first dice will be bigger than in the secon c) the sum of the numbers we get is smaller than five d) the multiplication of the numbers we get is an odd number plz help
In a different lottery, each ticket has 5 one-digit numbers 0-9 on it. (with no digit repeating twice) You win only if your ticket has the digits in the specific order of the winning numbers. e.g. if winning numbers are 1 2 3 4 5 then only tickets that specifically read 1 2 3 4 5 are winning tickets What are your chances of winning? I Select ]
Q1. Explain how Pascal's triangle may be used to identify the number of possible outcomes, based on five trials (i.e. n = 5). Derive an expression, based on a Binomial expansion, which shows the probability of each possible outcome. a)
14) There are 20 questions on an examination, and each student must answer 10 questions, including atleast 4 of the first 5 questions. How many different combinations of questions could a student choose toanswer?
Five cards are selected out of 52. In how many different ways can this be done if: they contain at least 4 clubs?
If you have 12 boxes then how many balls do you have to put randomly into the boxes in order to guarantee that some box will contain at least 4 balls?
3-digit numbers will be formed with the natural numbers from 1 to 5, without repeating any digita) How many numbers can be formed?b) How many numbers can be formed that start with 4?c) If one of the 3-digit numbers is selected, what is the probability that it starts with 1 and has 4 in the second position?
4) One number is randomly picked from 1 to 120. a) How many numbers are multiple of 3 or multiple of 5, or both? b) What is the probability to pick TWO numbers (no repeats), which are both "multiples of 3, but not multiples of 5?" Answer in (1 in ___)
4. A bag of fast-food sandwiches contains two hamburgers, four cheeseburgers, and three chicken burgers. If Wyatt ordered a cheeseburger and a chicken burger, what is the probability that a) the first sandwich selected will be one of his choices? b) neither of the first two sandwiches will be among Wyatt's choices? 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? 6. A pizza contains three toppings randomly selected from the following choices: pepperoni, mushrooms, green peppers, ham, bacon, and onions. Manuel enjoys all toppings, except bacon and onions. What is the likelihood that a pizza will contain a) no toppings that Manuel dislikes? b) exactly one topping that Manuel dislikes? c) at least one topping that Manuel dislikes? 7.…
Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is ? A) 16/19 B) 1 C) 3/2 D) 17/20

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