Please answer the following questions and show and explain how you got your answ
ID: 3303487 • Letter: P
Question
Please answer the following questions and show and explain how you got your answers(show all work):
1. Is it more probable to obtain at least one 6 in four throws of a fair die than it is to obtain at least one pair of 6's when two fair dice are thrown simultaneously 24 times?
2. William Stewart's four children come down for breakfeast at random times in the morning. What is the probability that they appear in order from the oldest to the youngest. Note: William Stewart does not have twins( nor triplets, nor quadruplets!)
3. The Computer Science Department at North Carolina State University wishes to market a new software product. The name of this package must consist of three letter's only.
(a.) How many possibilities does the department have to choose from?
(b.) How many possibilities are there if exactly one vowel is included?
(c.) How many possibilities are there if all three characters must be different and exactly one must be a vowel?
Explanation / Answer
1) probability to obtain at least one 6 in four throws =1-P( no six in four throws) =1-(5/6)4 =0.5177
probability to obtain at least one pair of 6's when two fair dice are thrown simultaneously 24 times =1-P( no pair in 24 times) =1-(35/36)24 =0.4914
hence true
2) total number of arrangements possible =4! =24
for they have only one favourable order, therefore probability that they appear in order from the oldest to the youngest =1/24
3)as each letter have 26 possibilities;l therefore total possibilities =263 =17576
b) possibilities are there if exactly one vowel is included = ( possibilities of 1 vowel and 2 different consonants +possibilities of 1 vowel and 2 same consonants ) =3!*5*21*20+3*5*20=12900
c)possibilities =3!*5*21*20 =12600