Rolling together percentages probabilities

[Vincent Vega]

Hi,

Wondering if you gals/guys could help me here.
For simplicity sake, say you have slot machine. To win the game all four balls must appear in four slots. Three of the balls are blue and one red. The 2nd slot is reserved for the blue ball. As for the red balls, they can only appear in the remaining slots, 1st, 3rd and 4th.

There's a fixed 10% chance that red will activate, there's only a 2% chance blue will activate. The event must be in that exact series for you to win.
I'm totally lost, and this is over my head assuming that "binomial distribution" is needed. How do I calculate these percentages together to find what the percentage of me winning that game would be.

a 10% followed by a 2% followed by a 10% followed by a 10%

$$0.10*0.02*0.10*0.10$$

 

[DaveC426913]

a 10% followed by a 2% followed by a 10% followed by a 10%

$$0.10*0.2*0.10*0.10$$

Not sure if your logic is right, but your math is wrong. 2% would be 0.02, not 0.2.

 

[Vincent Vega]

Not sure if your logic is right, but your math is wrong. 2% would be 0.02, not 0.2.

I tried typing that w/ the tex tags and it auto-filled that value?

 

[Vincent Vega]

Not sure if your logic is right, but your math is wrong. 2% would be 0.02, not 0.2.

edit never mind it edited it now. :)
how do you force it?

0.10*0.02*0.10*0.10

whoops, sorry for the double post

 

[CellCoree]

= 0.0002 or 0.02%

To calculate the overall probability of winning, we need to multiply the individual probabilities together. So, in this case, we have a 10% chance of the first slot being red, followed by a 2% chance of the second slot being blue, followed by a 10% chance of the third slot being red, and finally a 10% chance of the fourth slot being red. This gives us a total probability of:

0.10 * 0.02 * 0.10 * 0.10 = 0.0002 or 0.02%

This means that there is a 0.02% chance of winning the game with these specific conditions. However, keep in mind that this is assuming that each ball has an equal chance of being selected for each slot. If there are other factors at play, such as the weight of the balls or the mechanism of the slot machine, then the probabilities may be different. It's always important to consider all potential variables when calculating probabilities.