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zlopas [31]
3 years ago
9

If two fair dice are tossed, what is the smallest number of throws, n, for which the probability of getting at least one double

6 exceeds 0.5? (note: this was one of the first problems that de méré communicated to pascal in 1654.)
Mathematics
1 answer:
amid [387]3 years ago
3 0

This is a rather famous probability problem.

The easiest way to solve this is to calculate the probability that you WON'T roll a "double 6" (or a twelve) each time you roll the dice.  There are 36 ways in which dice rols can appear and only one is a twelve.  So, for one roll, the probability that you will NOT get a twelve is (35/36)^n where 35/36 is about .97222222 and n would equal 1 for the first trial.  So for your first roll the odds that you WON'T get a 12 is .97222222.

For the second roll we calculate (35/36) to the second power or (35/36)^2 which equals about .945216.

When we get to the 24th roll we calculate (.97222222)^24 which equals 0.508596.  

For the 25th roll, we calculate (.97222222)^25 which equals  0.494468.  For the first time we have reached a probability which is lower than 50 per cent.  That is to say, after 25 rolls, we have reached a point in which the probability is less than 50 per cent that we will NOT roll a twelve.

To phrase this more clearly, after 25 rolls we reach a point where the probability is greater then 50 per cent that you will roll a 12 at least once.

Please go to this page 1728.com/puzzle3.htm and look at puzzle 48. (The last puzzle on the page).  An intersting story associated with this probability problem is that in 1952, a gambler named Fat the Butch bet someone $1,000 that he could roll a 12 after 21 throws.  (He miscalculated the odds [as we know you need 25 throws] and after several HOURS, he lost $49,000!!!)

Please go that page and it has a link to the Fat the Butch story.


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Solve by graphing.
Tatiana [17]

Answer:

(2, 4)

General Formulas and Concepts:

<u>Algebra I</u>

  • Solving systems of equations by graphing

Step-by-step explanation:

Where the 2 lines intersect is the solution to the systems of equations.

6 0
3 years ago
De acuerdo con la tercera ley de movimiento planetario de Kepler, la masa de un planeta es directamente proporcional al cubo de
Sunny_sXe [5.5K]

Answer:

La masa del Sol es 2.509\times 10^{31} kilogramos.

Step-by-step explanation:

Tras una lectura cuidadosa al enunciado, tenemos que la Tercera Ley de Kepler queda descrita por la siguiente relación:

M \propto \frac{r^{3}}{T^{2}}

M = k\cdot \frac{r^{3}}{T^{2}} (Eq. 1)

Donde:

r - Distancia entre los centros del planeta y el satélite, medido en kilómetros.

T - Período oribital del satélite, medido en días.

k - Constante de proporcionalidad, medida en kilogramo-días cuadrados por kilómetro cúbico.

M - Masa del planeta, medida en kilogramos.

Podemos obtener la masa del Sol mediante la siguiente relación:

\frac{M_{S}}{M_{E}} = \frac{\frac{r_{E}^{3}}{T_{E}^{2}} }{\frac{r_{M}^{3}}{T_{M}^{2}} }

\frac{M_{S}}{M_{E}} = \left(\frac{T_{M}}{T_{E}} \right)^{2}\cdot \left(\frac{r_{E}}{r_{M}} \right)^{3} (Eq. 2)

Donde:

T_{M}, T_{E} - Períodos orbitales de la Luna y la Tierra, medidos en días.

r_{E}, r_{M} - Distancias entre la Tierra y el Sol, así como entre la Luna y la Tierra, medidas en kilómetros.

M_{S}, M_{E} - Masas del Sol y la Tierra, medidos en kilogramos.

Si M_{E} = 75.97\times 10^{24}\,kg, T_{E} = 365.3\,d, T_{M} = 27.3\,d, r_{M} = 3.84\times 10^{5}\,km y r_{E} = 1.496\times 10^{8}\,km, entonces tenemos que la masa del Sol es:

M_{S} = \left(\frac{T_{M}}{T_{E}} \right)^{2}\cdot \left(\frac{r_{E}}{r_{M}} \right)^{3}\cdot M_{E}

M_{S} = \left(\frac{27.3\,d}{365.3\,d} \right)^{2}\cdot \left(\frac{1.496\times 10^{8}\,km}{3.84\times 10^{5}\,km} \right)^{3}\cdot (75.97\times 10^{24}\,kg)

M_{S} = 2.509\times 10^{31}\,kg

La masa del Sol es 2.509\times 10^{31} kilogramos.

7 0
3 years ago
4.
RUDIKE [14]

Answer:

least possible number of sweets = lowest common multiple of 5,6 & 10 - 2

-I hope this helps! I got it figured out until near like the very end.-

-Please mark as brainliest!- Thanks!

5 0
3 years ago
Given two linear equations, explain how you can determine if the lines are parallel without graphing them
alexira [117]
Hello : 
let A and B two points in the first line calculate the slope : <span>:   (YB - YA)/(XB -XA)
</span>let C and D two points in the second line calculate the slop  (YC - YD)/(XC -XD)
you are slope 
7 0
4 years ago
What is the opposite integer of 10
NeX [460]
Since 10 is a positive the opposite must be negative. Opposite integer of 10 is -10 ( negative 10).

Happy studying ^-^
4 0
3 years ago
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