If George rolls the die 300 times, how many fives will he roll?
120 times.
300 times. In the ones place it occurs ten times per each 100 [5,15,25,...95] so 10x10 =100. Then in the tens place it also occurs ten times each 100 [50,51,52,53...59] We already counted 55 as one for the ones place and now we're counting 1 for the tens place. In the hundreds place, from 500 to 599 there are 100 fives (we already counted the tens and ones places. So 100 + 100 + 100 = 300.
The digit 9 appears in the units place 100 times from 1 to 1000 (9, 19, 29,..., 989, 999). It also appears in the tens place 100 times (90, 91, 92,..., 99, 190, 191,..., 199, 290,..., 999). Therefore, the digit 9 appears a total of 200 times from 1 to 1000.
Ratios and probabilityPerhaps this question is best answered with examples right off the bat. Let's say you have two regular fair dice (six-sided, of course). If you throw them 360 times and keep track of the numbers you throw, you'll record a seven about 60 times. So, you could say that the ratio of all possible numbers (including sevens) to sevens to is 360 to 36 (360:60), which is the same as 6 to 1 (6:1). You could also say that the ratio of all OTHER numbers (excluding sevens) to sevens to is 300:60, or 5:1.(there is no seven on a six sided die....)You would have also recorded about 50 occurrences of sixes, so you could say that the ratio of sevens to sixes is 60 to 50, or 6 to 5 (6:5). Obviously, the ratio of sixes to sevens would be 5:6.How about this:Let's say that the probability that a certain type of rare snake will have male offspring is 0.4. Obviously, the probability of the snake's having female offspring is 0.6. If the snake has lots of offspring, the ratio of males to females will be 0.4 to 0.6, which is the same as 4 to 6, which is the same as 2 to 3 (2:3). Stated another way, for every five snakes born, two will be male, and three will be female.By the way, whenever possible, it's a good idea to express ratios as close as you can to whole numbers, like 3:2 or 7:5. Also, whenever one of the digits is a one, it's particularly useful, like 3:1 or 9:1, or even 1.5:1. That last ratio, 1.5:1, is equal to 3:2. It depends on what you're more comfortable with.
The theoretical probability of rolling a 5 on a standard six sided die is one in six. It does not matter how many times you roll it, however, if you roll it 300 times, the theoretical probability is that you would roll a 5 fifty times.
The expectation is 50 times.
1/6 of all outcomes should be a 5. 300*1/6=50 This is the answer regardless of what you are rolling for. You would find whatever number you want and average about 50 times if you were to roll the dice 300 times. You might not get exactly 50, but it won't be far from that. There are faces on a die, and the odds of any one of those 6 numbers showing up is 1 out of 6 times. The above is only true if the dice are not rigged in any way ("loaded dice"). Now, if only one number likes to keep coming up, you might be dealing with loaded dice. In that case, the dice are made for cheating and the mathematical laws of average no longer apply.
If George rolls the die 300 times, how many fives will he roll?
1/6 or 300=4
1:6 or (theoretically) 50 times
1/6 of 300 = 50 times.
50
The probability of getting 3 is virtually 1. It is 1.76 septillionths less than 1.
The odds of rolling an even number (multiple of 2) is 1:2, so rolling 300 times will (theoretically) yield 150 even numbers.
Total possible outcomes of one roll = 6Number of primes on the die = 3 (2, 3, and 5)Probability of a prime on each roll = 3/6 = 50% .So, in 300 rolls of a fair die, you would expect approximately 150 primes.
The text of "Graceful Dice" says: Roll 1 six-sided die. The result is multiplied by 100 points and added to the ATKand DEF of all monsters youcontrol until the end of your turn. ...It is the result of the dice roll that is multiplied by 100. The result of the dice roll multiplied by 100 is then addedto your face-up monsters' ATK and DEF. Example Scenario: # You have one "Dark Magician" (2500 ATK / 2100 DEF) and one "Kuriboh" (300 ATK / 200 DEF) on your side of the field. # Activate "Graceful Dice" and the result of the dice roll is a 5. # 5 x 100 = 500 # 500 ATK and 500 DEF are added to "Dark Magician" and "Kuriboh" # "Dark Magician" new stats: (3000 ATK / 2600 DEF) & "Kuriboh" new stats: (800 ATK / 700 DEF)