Please answer the following questions and show and explain how you got your answ
ID: 3303488 • Letter: P
Question
Please answer the following questions and show and explain how you got your answers:
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
Question 1:
Probability of obtaining at least one 6 in four throws of a fair die is computed as:
= 1 - Probability of obtaining no six in four throws of a fair die
= 1 - ( 5/6 )4
because probability of not getting a 6 in a dice throw is (5/6)
= 0.5177
Therefore 0.5177 is the required probability here.
Now the probability of getting a pair of 6s in 2 dice throws is computed as: (1/6)2 = 0.0278
Now when the pair of dice is thrown 24 times, probability of obtaining at least a pair of 6s in a pair of dice throws out of 24 times is computed as:
= 1 - (1 - 0.0278)24
= 0.4914
Therefore 0.4914 is the required probability here.
Therefore, it is 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