The combination to a lock consists of a sequence of three numbers in the range 0-28.a) How many combinations are possible in which no two consecutive numbers can be the same?b) How many combinations are possible in which all three numbers are different?c) What is the probability that the combination of a randomly-chosen lock consists of three different numbers?d) What is the probability that the combination of a randomly-chosen lock contains at least one repeated number?a) If no two consecutive numbers can be the same, write the expression (consisting of a product of numbers) that represents the number of possiblecombinations.(Do not simplify.)Thus, if no two consecutive numbers can be the same, the number of combinations is(Simplify your answer.)b) If all three numbers are different, the number of combinations is(Simplify your answer.)c) The probability that the combination of a randomly-chosen lock consists of three different numbers is(Round to two decimal places as needed.)d) The probability that the combination of a randomly-chosen lock contains a repeated number is(Round to two decimal places as needed.)

Solution Given That, The combination to a lock consists of a sequence of three numbers in the range…

Answered: The combination to a lock consists of a…

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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A player is dealt 3 cards from a standard 52-card deck. Determine the probability of being dealt two of a kind (such as two aces or two kings) by answering questions a through d. ... a) How many ways can 3 cards be selected from a 52-card deck? There are ways that 3 cards can be selected from a 52-card deck. (Type a whole number.) b) Each deck contains 4 twos, 4 threes, and so on. How many ways can two of the same card be selected from the deck? There are ways that two of the same card can be selected from the deck. (Type a whole number.) c) The remaining card must be different from the 2 chosen. After selecting the two of a kind, there are 12 different ranks of cards remaining in the deck that can be chosen. Of the 12 ranks remaining, the player chooses 1 of them and then selects one of the 4 cards in the chosen rank. How many ways can the player select the remaining card? There are ways the player can select the remaining card. (Type a whole number.)
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)
Six digits are chosen randomly from the set {0, 1,2,.....9). a.) What is the probability that all six digits are the same? b.) What is the probability that only 2 digits are the same?
Four fair eight-sided dice are rolled. An outcome is an ordered sequence of 4 numbers between 1 and 8. For example, the sequence 1-1-4-3 is different from the sequence 4-1-3-1. a) How many outcomes are possible? b) What is the probability that a roll results in 4 different numbers? c) What is the probability that a roll results in 4 of the same number? a) The number of possible outcomes is (Simplify your answer.) b) The probability that a roll results in 4 different numbers is (Type an integer or decimal rounded to four decimal places as needed.) c) The probability that a roll results in 4 of the same number is (Type an integer or decimal rounded to seven decimal places as needed.)
a) A box contains 18 batteries, out of which 5 are defective. If 3 fuses are selected at random from this box what is the probability that i. All 3 are defective ii. One of them is defective
PigeonHole principle A drawer holds a dozen brown socks and a dozen black socks, both of which are unmatched. In the dark, a man pulls socks at random. a) How many socks does he need to remove to ensure that he has at least two socks of the same color? b) How many socks does he need to pull out to ensure he has at least two black socks?
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 ___)
each of the natural numbers from 1 to 15 inclusive is written on one card, and different numbers are written on the different cards. We randomly select four cards. What is the probability that the smallest number of selected cards is 8 or the largest of them is 12?
In a certain lottery, an urn contains balls numbered 1 to 25. From this urn, 4 balls are chosen randomly, without replacement. For a $1 bet, a player chooses one set of four numbers. To win, all four numbers must match those chosen from the urn. The order in which the balls are selected does not matter. What is the probability of winning this lottery with one ticket? The probability of winning is (Use scientific notation. Use the multiplication symbol in the math palette as needed. Round to the nearest hundredth as needed.)
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
By mistake six burned out light bulbs (B) have been mixed up with 4 good (G) ones. If a random sample of three is drawn, what is the probability a) that all will be good? b) at least 1 is burned out? c) at most 2 are burned out? d) Show the arithmetic of the probability that exactly 2 are good and 1 is bad.
In a lottery, you select 5 numbers from 1- 50, 5 numbers are drawn by the lottery, if they match all the 5 numbers you selected, you win the Jackpot. Each lottery is independent. Each time you play you need to pay £1. a)You play this lottery every day for three 365-day years. The probability that you win the Jackpot twice is : b)There are 10 million people playing this lottery like you do ( once a day for three 365-day years), the probability at least one person win the Jackpot twice is: c)ln order to be at least 1.0% sure that you can win the Jackpot at least once, what is the minimum number of year you need to play if you play once a day? (Put down an integer) d)Assume there is no other prize except the Jackpot. If you are risk neutral, you will not play the lottery if the Jackpot prize is below

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