Assume that the year has 366 days and all birthdays are equally likely. a) What is the probability that two people chosen at random were born on the same day of the week? b) What is the probability that in a group of n people chosen at random, there are at least two born on the same day of the week? c) How many people chosen at random are needed to make the probability greater than 1/2 that there are at least two people born on the same day of the week?

1 answer
Question:

Assume that the year has 366 days and all birthdays are equally likely.
a) What is the probability that two people chosen at random were born on the same day of the week?
b) What is the probability that in a group of n people chosen at random, there are at least two born on the same day of the week?
c) How many people chosen at random are needed to make the probability greater than 1/2 that there are at least two people born on the same day of the week?

Answers

Answer:The answers to the question area) [tex]\frac{1}{7}[/tex]b) Where n >7 the probability = 1 n = 7 it is 0.99388n = 6 it is 0.95716n = 5 it is 0.850062 n = 4 it is 0.65n = 3 it is 0.38776n = 2 it is 0.14286n = 1 it is 0c) n > 3 where n is an integerStep-by-step explanation:The probability for the first person to be born on  a certain day is 1P(Week Birth Day) = 7/7 = 1The probability for the second person to be born on the same day as the first person is P(Week Birth Day Second l Week Birth Day) = 1/7By conditional probability, we have P(B|A) = [tex]\frac{P(AnB}{P(A)}[/tex] that is [tex]\frac{1*\frac{1}{7} }{1} = \frac{1}{7}[/tex] (b) Since there 7 days in a week, the probability that in a group of n people chosen at random, there are at least two born on the same day of the week where n ≥ 8 is 1 as there must be two people born on the same dayP(A) = 1 when n ≥ 8The probability that at least two were born on the same day when n < 8 then there are Number of ways to choose the birthday of first person = 7Number of ways to choose the birthday of second person = 6Number of ways to choose the birthday of third person =5and so on till we haveNumber of ways to choose the birthday of seventh person = 1P(At least 2 born on the same day) can then be found by the complement rule thus Let P(At least 2 born on the same day)  = P(A)Then we have P(A) = 1 - P(A)' where P(A)'  = P (No 2 born on the same day)Thus we have P(A) = 1 - [tex]\frac{7}{7} *\frac{6}{7}* \frac{5}{7} *\frac{4}{7} *\frac{3}{7}* \frac{2}{7} *\frac{1}{7}[/tex]  = 1 - [tex]\frac{720}{117649}[/tex] = 0.99388n = 6 we have P(A) = 1 - [tex]\frac{7}{7} *\frac{6}{7}* \frac{5}{7} *\frac{4}{7} *\frac{3}{7}* \frac{2}{7}[/tex]  =  1 - [tex]\frac{720}{117649}/\frac{1}{7}[/tex]  =1 - [tex]\frac{720}{16807}[/tex] =0.95716n = 5 gives P(A) =1 - [tex]\frac{7}{7} *\frac{6}{7}* \frac{5}{7} *\frac{4}{7} *\frac{3}{7}[/tex] =  1 - [tex]\frac{720}{16807}/\frac{2}{7}[/tex] =   1- [tex]\frac{360}{2401}[/tex] = 0.850062 n = 4  P(A) =1 - [tex]\frac{7}{7} *\frac{6}{7}* \frac{5}{7} *\frac{4}{7}[/tex] = 1 - [tex]\frac{360}{2401} / \frac{3}{7}[/tex] =   1 - [tex]\frac{120}{343}[/tex] = [tex]\frac{223}{343}[/tex] = 0.65n = 3  P(A) =1 - [tex]\frac{7}{7} *\frac{6}{7}* \frac{5}{7}[/tex]  =   1 - [tex]\frac{120}{343}*\frac{7}{4}[/tex] = 1 -[tex]\frac{30}{49}[/tex] = [tex]\frac{19}{49}[/tex] = 0.38776n = 2  P(A) =1 - [tex]\frac{7}{7} *\frac{6}{7}[/tex]  = 1 -[tex]\frac{30}{49}*\frac{7}{5}[/tex] = [tex]\frac{1}{7}[/tex] = 0.14286(c) For the probability to be greater than half that there are at least two people born on the same day of the week is given by n = 4,  P(A) = 0.65n = 3,  P(A) = 0.38776Therefore for a probability greater than 4, n should be > 3n > 3

Similar Solved Questions

1 answer

ABC Corporation has total assets of 120 million, total liabilities of 80 million, Goodwill of 12 million, and 4 millions of shares outstanding. If you believe the reasonable price to tangible book value should be 1.6 for this company, what is the implied share price of ABC

ABC Corporation has total assets of 120 million, total liabilities of 80 million, Goodwill of 12 million, and 4 millions of shares outstanding. If you believe the reasonable price to tangible book value should be 1.6 for this company, what is the implied share price of ABC...
2 answers

Its seventh grade algebra pls help Chuck E Cheese offers birthday parties for a fee of $250 plus $5 per person. If you can spend no more than $400 on your party, write an inequality to find the maximum number of people who can attend the party? I

its seventh grade algebra pls help Chuck E Cheese offers birthday parties for a fee of $250 plus $5 per person. If you can spend no more than $400 on your party, write an inequality to find the maximum number of people who can attend the party? I...
1 answer

Factor by grouping 20i^3-25i^2+4i-5

factor by grouping 20i^3-25i^2+4i-5...
2 answers

Two competing internet companies have recently restructured their payment plans. Quick Net requires a $10 activation fee and charges $55 per month for their basic plan. Speedy Net requires no activation fee and charges $57 per month for their basic plan. When will the two plans be equal in cost?

Two competing internet companies have recently restructured their payment plans. Quick Net requires a $10 activation fee and charges $55 per month for their basic plan. Speedy Net requires no activation fee and charges $57 per month for their basic plan. When will the two plans be equal in cost?...
1 answer

Hello i need help with this plz

hello i need help with this plz...
2 answers

Ben and Jerry went for a drive. They decided to stop for a snack and have some ice cream. How fast did they drive on their way to the store? A) 15 km/h B) 30 km/h C) 40 km/h D) 60 km/h

Ben and Jerry went for a drive. They decided to stop for a snack and have some ice cream. How fast did they drive on their way to the store? A) 15 km/h B) 30 km/h C) 40 km/h D) 60 km/h...
1 answer

How to write a good discussion question for a science prac or IA? give me tips please. I will do whatever you ask.

How to write a good discussion question for a science prac or IA? give me tips please. I will do whatever you ask....
1 answer

Five out of every six girls in 6th grade completed homework if there are 48 girls in 6th grade how many girls completed homework

Five out of every six girls in 6th grade completed homework if there are 48 girls in 6th grade how many girls completed homework...
1 answer

Does the equation below represent a relation, a function, both a relation and a function or neither y = x2 – 9x

Does the equation below represent a relation, a function, both a relation and a function or neither y = x2 – 9x...
1 answer

What is the factorization of the following trinomial? 15x2 - 44x - 36 (5x - 9)(3x + 4) (3x - 4)(5x + 9) (5x - 18)(3x + 2) (5x + 18)(3x - 2)

What is the factorization of the following trinomial? 15x2 - 44x - 36 (5x - 9)(3x + 4) (3x - 4)(5x + 9) (5x - 18)(3x + 2) (5x + 18)(3x - 2)...
1 answer

The place of an item that is sold for $540 was reduced by 33 1 over3% by what percent match the price of an item be increased to bring the price back up to $540

The place of an item that is sold for $540 was reduced by 33 1 over3% by what percent match the price of an item be increased to bring the price back up to $540...
1 answer

Need help with question 3 please

Need help with question 3 please...
1 answer

While observing a new client perform the pushing assessment, the personal trainer notices that his head protrudes forward. Which of the following groups of muscles are probably overactive? A. middle trapezius B. erector spinae C. rhomboids D. levator scapulae

While observing a new client perform the pushing assessment, the personal trainer notices that his head protrudes forward. Which of the following groups of muscles are probably overactive? A. middle trapezius B. erector spinae C. rhomboids D. levator scapulae...
1 answer

An Actor with *blank* his part will pretend. A.)Dessert B.)Criticism C.)Editor D.)Humor

An Actor with *blank* his part will pretend. A.)Dessert B.)Criticism C.)Editor D.)Humor...
1 answer

What is the approximate weight of a 20-kg cannonball on the moon if the acceleration due to gravity is 1.6 m/s2? 2 N 20 N 32 N 196 N

What is the approximate weight of a 20-kg cannonball on the moon if the acceleration due to gravity is 1.6 m/s2? 2 N 20 N 32 N 196 N...
1 answer

Dependency is an emotion defined by the expression of affection, respect and concern

Dependency is an emotion defined by the expression of affection, respect and concern...
1 answer

What games do you play? Be sure not to report any answers!

What games do you play? Be sure not to report any answers!...
1 answer

Jess gave her a ​$4.90 tip. The tip was 7​% of the cost of the . Write an equation to find​ b, the cost of the Manicure If all percents are expressed as​ decimals, the equation (fill in the blank) can be used to find​ b, the cost of the manicure .

Jess gave her a ​$4.90 tip. The tip was 7​% of the cost of the . Write an equation to find​ b, the cost of the Manicure If all percents are expressed as​ decimals, the equation (fill in the blank) can be used to find​ b, the cost of the manicure ....
2 answers

When I triple my number and add five I get twenty six what is my number

When I triple my number and add five I get twenty six what is my number...

-- 0.059127--