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.
Answer:
9
Step-by-step explanation:
Slope = Change in Y / change in x
Slope = (16 - -9) / (-2 - 3)
Slope = 25/-5
Slope = -5
<span>-7 • (a4 - 81a2 - 162)27
-------------------------------- hope it helps
27</span>
Answer:$6451.6 should be deposited.
Step-by-step explanation:
The principal was compounded monthly. This means that it was compounded 12 times in a year. So
n = 12
The rate at which the principal was compounded is 7.2%. So
r = 7.2/100 = 0.072
It was compounded for 3 years. So
t = 3
The formula for compound interest is
A = P(1+r/n)^nt
A = total amount in the account at the end of t years. A is given as $8000 Therefore,
8000 = P (1+0.072/12)^12×3
8000 = P(1+0.006)^36
8000 = P(1.006)^36
P = 8000/1.24
P = $6451.6
