Five different CD-Rom games: garble, trapster,zoom, bungie, and blast'em are offered as a promotion by SugrRush cereals. One game is randomly included ith each box of cereal.
Determine the probability of getting all 5 games if 12 boxes are purcahsed.
why don't you explain??!!!???
The formula The Wizard used was
1 - 5*(4/5)^12 + 10*(3/5)^12 - 10*(2/5)^12 + 5*(1/5)^12.
See if you can understand the logic. The (4/5)^12 term is the probability that one of the five types is missing. The remaining terms take into account the probability that two, three or four types are missing. There are ten ways of choosing the two or three that may be missing, but only five ways of choosing the one or four types that may be missing.
The answer of The Wizard of Odds is correct. For an explanation of how it was arrived at, see the "Roulette board (0,00)" question at
http://wizardofodds.com/askthewizard/197
The same method was used.
Well, let's break it down. There are 5 different CD-Rom games offered by SugrRush cereals. And one game is included randomly in each box of cereal.
So, for the first box, the probability of getting any specific game is 1 out of 5, since there are 5 games in total. Similarly, for the second box, the probability is also 1 out of 5.
Since each box is selected independently, we can multiply the probabilities together. So, for the first two boxes, the probability of getting any specific game in both boxes is (1/5) * (1/5) = 1/25.
Using the same logic, for the first three boxes, the probability of getting any specific game in all three boxes is (1/5) * (1/5) * (1/5) = 1/125.
So, for 12 boxes, we can continue this pattern. The probability of getting any specific game in all 12 boxes is (1/5)^12 = 1/244,140,625.
However, since we want to find the probability of getting all 5 games, we need to consider the total number of different possibilities. There are 5 games in total, and each game can be chosen independently for each box.
So, the total number of possibilities is 5^12 = 244,140,625.
Therefore, the probability of getting all 5 games if 12 boxes are purchased is 1/244,140,625.
It's quite a small probability. You might have better luck finding a pot of gold at the end of a rainbow, or discovering that your socks always stay matched in the laundry!
To determine the probability of getting all 5 games when purchasing 12 boxes of cereal, we need to calculate the probability of obtaining each game individually and then multiply them together.
First, let's calculate the probability of getting each game in a single box of cereal.
There are 5 games in total, so the probability of getting a specific game in a single box is 1/5.
Next, we need to calculate the probability of not getting a specific game in a single box. Since there are 5 games, the probability of not getting a specific game is 4/5.
Now, let's calculate the probability of getting all 5 games in 12 boxes of cereal.
To obtain all 5 games, we need to multiply the probability of getting each game in a single box together. Since we are purchasing 12 boxes, we multiply this probability by itself 12 times.
Probability of getting all 5 games in a single box = (1/5) * (1/5) * (1/5) * (1/5) * (1/5) = 1/3125
Probability of not getting all 5 games in a single box = (4/5) * (4/5) * (4/5) * (4/5) * (4/5) = 1024/3125
To find the probability of getting all 5 games in 12 boxes, we raise the probability of getting all 5 games in a single box to the power of 12.
Probability of getting all 5 games in 12 boxes = (1/3125)^12 = 1/1220703125000
Therefore, the probability of getting all 5 games when purchasing 12 boxes of cereal is 1 in 1,220,703,125.