So, first establish a ratio
x:y, x/y, or x to y
for number 9, that's gonna be 1 yards:.914 meters
You need to find what you get for meters (y) when you have 4 yards
Fill into the x slot in the proportion (ratio)
4:y as 1:0.914
You can do this in a few ways
- you can "cross multiply" by putting each ratio into a fraction form
1/0.914 * 4/y
-Or, when you are dealing with a term based on a single unit (the single yard measurement), then you can take a little shortcut and just multiply the denominator by 4.
You get 0.914*4= 4.914m
For the second one, we need to establish how many marbles there are, or your "pool"
4+3+2+1= 10
Then, your chances of drawing a certain color is how many of that color you have over your total pool.
1/10 or .1 is your probability of drawing a white marble first.
Then, since you replace it and draw again, you repeat this process and multiply.
1/10*1/10=1/100 or .1*.1= 0.01 is your probability of drawing a white both times.
*Note: If the marble is not returned, the pool changes from 10 to 9 because that marble is no longer in the pool.
For the last one, we know that a cube has six sides, all different numbers. That makes each number's probability 1/6.
Now into the more complicated stuff.
Since you are rolling 2 dice and you are looking for a sum of <6
Draw a chart of all the possible outcomes
D1) 123456
D2) 123456
Make a chart, the possible rolls for each die going on the top and side, then simply add in a box fashion ie. 2+2=4, 3+5=8, etc. and the most that can be rolled is 12
1.2,3,4,5,6
2,4,5,6,7,8
3,5,6,7,8,9
4,6,7,8,9,10
5,7,8,9,10,11
6, 8,9,10,11,12
now draw a diagonal line through all the sixes, the ones you need less than, and get rid of everything above that, along with the one because you can't add to get a 1 from two dice
2,3,4,5,6
2,4,5,6
3,5,6
4,6
5,6
6
How many different combinations can you roll below six?
11
Now multiply 6*6 to get 36 (all of the possible rolls)
and put the number 11 over it
11/36
Reduce if needed, which it isn't in this case
The probability that the roll adds up to a number less than 6 is 11/36
