Could a probability guru help me determine the odds of hitting this slots jackpot?

Hello. I am trying to determine my chances of winning the prize of a particular slot machine.

The slot has a haunted mansion theme, and the top prize is achieved by finding each of five ghosts during a bonus round. Here is how it works:

Three or more bonus symbols initiate the bonus round. Two or more bonus symbols end a bonus round in progress.

There are five different characters within the mansion - a maid, Butler, grandma, little girl, and master. If three of the same character appears during a single spin within the bonus round, the “ghost” of the character is uncovered. If all five unique ghosts are uncovered during the bonus, the prize is awarded.

If we assume the following, based on my observations of thousands of spins:

The maid ghost appears about 1 in 100 spins. The butler 1 in 50. The grandma 1 in 25. The master 1 in 10. The little girl also 1 in 10. All five events must occur during a bonus round. Three or more bonus symbols seem to occur 1 in 50. 2 or more bonus symbols seem to occur maybe 1 in 10.

In case there is confusion, the same bonus symbol which initiates the bonus, ends the bonus phase when appearing during said bonus.

Could anyone help me estimate the odds of winning the jackpot? They must be astronomically low. Thank you very much.

Since no one has chimed in yet, I will share my thoughts.

Assuming: .02 chance to hit the bonus, .01 chance to find the maid x .9 chance bonus does not end, .02 x .9 for the butler, .04 x .9 for the grandma, .1 x .9 for little girl, .1 x .9 for master...

.01 x .9 x .02 x .9 x .04 x .9 x .1 x .9 x .1 x .9 x .02

This is approximately a 1 in a billion chance. However, true jackpot odds must be somewhat higher since it is possible to spin more than 5 times in the bonus. This is where I am stuck.

If I knew how to determine the following maybe I could figure out the rest.

If an event has a 1 in 10 probability of occurring per attempt, and 10 attempts are made, what is the probability of the event happening at least once?

Quote: littlelostbunny

<snip>If I knew how to determine the following maybe I could figure out the rest.

If an event has a 1 in 10 probability of occurring per attempt, and 10 attempts are made, what is the probability of the event happening at least once?

littlelostbunny,

This is an elementary problem. One easy way to calculate the result is to realize that these two outcomes

1. Win one or more times (let's call this W1+)
2. Lose all 10 attempts (let's call this L10)

are related by the equation W1+ + L10 = 1. Thus, we can calculate the desired result as W1+ = 1 - L10.

Now to lose all 10 attempts, we have to lose the first one: since we win 1/10 = 0.1, we lose 9/10 = 0.9.

Then we have to lose the second attempt: this will also occur with frequency 0.9. Since we have to lose both attempts, the overall probability of losing the first two attempts is 0.9^2 = 0.81.

Similarly, we subsequently have to lose the third, fourth, ... and tenth times.

Thus, the probability of losing all 10 attempts is

L10 = 0.9^10 = 0.348678..., or nearly 35% of the games.

Therefore, we'll win at least one of the 10 attempts the remaining W1+ = 1 - 0.348678... = 0.651321..., or just over 65% of the games.

Hope this helps!

Dog Hand