There are 12 signs of the zodiac. How many people must be present for there to...

There are 12 signs of the zodiac. How many people must be present for there to be at least a 50% chance that two or more of them were born under the same sign?

1-P(no one has the same sign) >= 0.5

P(two or more people have the same sign) = 1-P(no one has the same sign)

= 1 - (12!/(12-n)!)/12^n

1-0.5=0.5 >= P(no one has the same sign) = 12!/(12^n * (12-n)!)

0.5 >= 12!/(12^n * (12-n)!)

Solve for n.

n = 5

My question is, why is the probability that no one has the same sign? Could you explain in detail how do you arrive to (12!/(12-n)!)/12^n)?

Expert Solution

TOPIC:Classical definition of probability.

orchestra answered 2 years ago

For a 4 mile by 4 mile grid, how many signs must be placed to ensure...

For a 4 mile by 4 mile grid, how many signs must be placed to ensure that the farthest distance between two signs is LaTeX: \sqrt[]{2} 2 miles?

1) How many people were present for the signing of the Declaration of Independence?

Descartes' Rule of signs Use Descartes' Rule positive and how of Signs to determine how many...

Descartes' Rule of signs Use Descartes' Rule positive and how of Signs to determine how many negative real zeros of the polynomial can have. Then determine the possible total number of real zeros. P(x) = x^3 - x^2 - x - 3 P(x) = 2x^3 - x^2 + 4x -7 P(x) = 2x^6 + 5x^4 - x^3 -5x -1 P(x) = x^4 + x^3 + x^2 + x + 12 P(x) = x^5 + 4x^3 - x^2 + 6x P(x)...

How many calories of heat must be added to 12 grams of ice at -50 oC...

How many calories of heat must be added to 12 grams of ice at -50 oC to convert it to 12 grams of steam at 100 oC.

Investors are considering funding of new video games. How many people must be surveyed in order...

Investors are considering funding of new video games. How many people must be surveyed in order to be 95% confident that the estimated percentage is within 4% points of the true population percentage? A.) Assume nothing is known about percentage of people who play video game. B.) Assume that 16% of people play video game.

How many ways can 11 Redcoat basketball players and Coach Woodburn (12 people) be arranged along...

How many ways can 11 Redcoat basketball players and Coach Woodburn (12 people) be arranged along the sidelines? a) with no restrictions. b) if Coach Woodburn must be at one end of the bench? c) if Travis and Pat must stand together? d) if Travis, Pat, and Woody must stand together? e) if Travis and Pat must be kept separated?

1.) how many mole of oxygen atoms are present in 5.36g of CaCo3? 2.) how many...

1.) how many mole of oxygen atoms are present in 5.36g of CaCo3? 2.) how many moles of Cl atoms are there in 1.7g of CCl4 3). What is the mass of 2.4x10^29 particles of CaCo3? 4.) In the reaction below, (CH4+2O2----> CO2 +2H2O) how many moles of CH4 are required to react with 0.5 mol of oxygen gas to form products? 5). Consider the reaction of 3 mol of P4 and 10 mol of oxygen gas to produce P2O5....

How many GRAMS of carbon are present in 4.00 moles of carbon dioxide, CO2? How many...

How many GRAMS of carbon are present in 4.00 moles of carbon dioxide, CO2? How many MOLES of oxygen are present in 3.11 grams of carbon dioxide? How many GRAMS of oxygen are present in 9.82×10^22 molecules of tetraphosphorus decaoxide?

a. How many people must be surveyed to obtain the percent of the population that has health insurance to within 4% with 90% confidence?

a. How many people must be surveyed to obtain the percent of the population that has health insurance to within 4% with 90% confidence? b. How many subjects must be sampled to estimate the mean annual expense of a family on cell phones to within $4 with 99% confidence. Assume the population standard deviation is $9.

how many Ba^2+ ions and how many AsO4^3- ions are present in a 10.0g sample of...

how many Ba^2+ ions and how many AsO4^3- ions are present in a 10.0g sample of Ba3(AsO4)3-

Question