Question

In: Math

1. If all the letters of the word ABOUT are arranged at random in a line,...

1. If all the letters of the word ABOUT are arranged at random in a line, find the probability that the arrangement will begin with AB...

2.

The odds of throwing two fours on a single toss of a pair of dice is 1:35
What is the probability of not throwing two fours? (Hint: there are 2 conversions here)

All answers are written as fractions for consistency....

Select one:

a. 35/36

b. 1/36

c. 1/35

d. 35/1

Expert Solution

1.

Number of possible words possible if all the letters of the ABOUT are arranged in a line = 5x4x3x2x1 = 120

(First position can be any of the 5 letters;

Oncee first position is filled ; remaining letters are four;

second position can be filled with any of the remaining four letters ;

third position - any of 3 letter ; 4th position - any of 2 letters ; 5th position - 1 letter; i.e 5x4x3x2x1)

As the arrangement will begin with AB, Number possible ways of arranging remaining 3 letters in the remaining positions =3x2x1=6

Therefore,

probability that the arrangement will begin with AB = 6/120 = 1/20=0.05

2.

The odds of throwing two fours on a single toss of a pair of dice is 1/35:

i.e

Number of outcomes favorable for the event of two fours on a single toss of a pair of dice = 1

Number of outcomes not favorable for the event of two fours on a single toss of a pair of dice = 35

Total number of outcomes

= Number of outcomes favorable for the event of two fours on a single toss of a pair of dice

+ Number of outcomes not favorable for the event of two fours on a single toss of a pair of dice =1+35=36

probability of not throwing two fours

= Number of outcomes favorable for the event of not throwing two fours on a single toss of a pair of dice / Total number of outcomes

Number of outcomes favorable for the event of not throwing two fours on a single toss of a pair of dice = Number of outcomes not favorable for the event of two fours on a single toss of a pair of dice = 35

probability of not throwing two fours

= Number of outcomes favorable for the event of not throwing two fours on a single toss of a pair of dice / Total number of outcomes = 35/36

probability of not throwing two fours =35/36

Answer :

a.35/36

milcah answered 2 hours ago

If all permutations of the letters of the word "BEFORE" are arranged in the order as...

If all permutations of the letters of the word "BEFORE" are arranged in the order as in a dictionary. What is the 32 word?

The letters of the word product are arranged in all possible ways. If an arrangement is...

The letters of the word product are arranged in all possible ways. If an arrangement is picked at random. What is the probability that the arrangement will start with p and ends with a vowel?

2)The letters of the word EXCELLENT are arranged in a random order. Find the probability that:...

2)The letters of the word EXCELLENT are arranged in a random order. Find the probability that: a. the same letter occurs at each end. b. X,C, and N occur together, in any order. c. all 9 letters occur in alphabetical order.

1) Find the number of unique ways that the letters in the word can be arranged:...

1) Find the number of unique ways that the letters in the word can be arranged: KERFUFFLE 2) A survey of commuters found that 313 owned a motorcycle, 232 owned a car, 269 owned a moped, 98 owned a car and a moped, 57 owned only a car, 104 owned a motorcycle and moped but not a car, 69 owned all three, and 64 owned none. What proportion of people surveyed owned only a moped? Leave your answer as an...

a) How many ways can the letters of the word COMPUTER be arranged in a row?...

a) How many ways can the letters of the word COMPUTER be arranged in a row? b) How many ways can the letters of the word COMPUTER be arranged in a row if O and M must remain next to each other as either OM or MO? c) How many permutations of the letters COMPUTER contain P, U and T (all three of them) not to be together in any order?

55) A) In how many dierent ways can the letters of the word 'JUDGE' be arranged...

55) A) In how many dierent ways can the letters of the word 'JUDGE' be arranged such that the vowels always come together? B) How many 3 digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9 which are divisible by 5 and none of the digits is repeated? C) In how many ways can 10 engineers and 4 doctors be seated at a round table without any restriction? D) In how many ways can...

A machine prints a word and the number of letters in this word is a Poisson...

A machine prints a word and the number of letters in this word is a Poisson distributed random variable with parameter λ (so it could possibly have zero letters). However, each letter in the word is printed incorrectly with probability 2/3 independently of all other letters. Compute the expectation and the variance of the number of incorrect letters in the word that the machine prints.

A word is said to be “abecedarian” if the letters in the word appear in alphabetical...

A word is said to be “abecedarian” if the letters in the word appear in alphabetical order. For example, the following are all six-letter English abecedarian words: abdest, acknow, acorsy, adempt, adipsy, agnosy, befist, behint, beknow, bijoux, biopsy, cestuy, chintz, deflux, dehors, dehort, deinos, diluvy, dimpsy Write a method called isAbecedarian that takes a String and returns a boolean indicating whether the word is abecedarian.

Write a program that will read a line of text. Display all the letters that occure...

Write a program that will read a line of text. Display all the letters that occure in the text, one per line and in alphabetical order, along with the number of times each letter occurs in the text. Use an array of base type int of length 26, so that the element at index 0 contains the number of a’s, the element at index 1 contains the number of b’s, and so forth, Alloow both upperCase and lower Case. Define...

A random rearrangement doe not separate out between repeated letters. Consider word CHRISTMASTIME. a) What's the...

A random rearrangement doe not separate out between repeated letters. Consider word CHRISTMASTIME. a) What's the expected # vowels in first three letters of random rearrangement of CHRISTMASTIME? b) What's probability that all the S's happen before all the I's in random rearrangement of CHRISTMASTIME? c) What's probability that word CHRIST happens in consecutive letters of uniform rearrangement of CHRISTMASTIME?