Question: Please answer the following questions and show and explain how you got

Question

Question: Please answer the following questions and show and explain how you got your answers: 1. Is it mor...

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

(1)

Probability of obtaining atleast one 6 in four throws of die = 1-(5/6)4 = 0.518

Probability of obtaining at least one pair of 6's when two fair dice are thrown simultaneously 24 times = 1-(35/36)24

= 0.491

So, it is more probable to obtain at least one 6 in four throws of a fair die.

(2)

Since there are 4 children, so total possible permutations = 4! = 24

So, the probability that the four children appear in the particular order from oldest to youngest = 1/24

Hope this helps !

Related Questions

Navigate

• Browse (All)
• Browse Q
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.