How to calculate the overall odd of multiple percentages not happening in a row?

[MarcSim88]

Hi All,
I have no idea how to do this so I wanted to ask the community.
I play card games as a hobby and would like to know how to calculate the percentages of not drawing certain cards in a row.

So the situation was as this:
My deck of cards had 16 cards in it,
11 of the cards won me the game in the moment if I drew them and 5 did not.

I got 4 turns of drawing any of the 11 cards out of 16 to win the game in the moment.

4 Turns went by and I didn't draw any of the 11 out of 16 cards in the deck I needed and lost the game because of it

Individual probabilities were as such:

11/16 (First turn) - Miss - 67.85% probability to draw one of the cards I needed
12/16 (Second turn) - Miss - 75% probability to draw one of the cards I needed
13/16 (Third turn) - Miss - 81.25% probability to draw one of the cards I needed
14/16 (Fourth turn) - Miss - 87.5% probability to draw one of the cards I needed

My question is,
How do I calculate the overall % of the 4 turns of not drawing 1 of the 11 cards I needed

In a row odds of 67.85%, Into 75%, Into 81.25%, Into 87.5%

Is it possible to calculate this?

Many thanks for any help
-Marc

 

[BigBeachBanana]

Individual probabilities were as such:

11/16 (First turn) - Miss - 67.85% probability to draw one of the cards I needed
12/16 (Second turn) - Miss - 75% probability to draw one of the cards I needed
13/16 (Third turn) - Miss - 81.25% probability to draw one of the cards I needed
14/16 (Fourth turn) - Miss - 87.5% probability to draw one of the cards I needed

My question is,
How do I calculate the overall % of the 4 turns of not drawing 1 of the 11 cards I needed

I don't believe your calculation here is correct. Are you replacing the card back into the deck after every draw?

 

[MarcSim88]

I don't believe your calculation here is correct. Are you replacing the card back into the deck after every draw?

I'm not sure If I can edit the OP, won't let me, but yes apologies I misswrote the fractions.

11/16 (First turn) - Miss - 67.85% probability to draw one of the cards I needed
11/15 (Second turn) - Miss - 75% probability to draw one of the cards I needed
11/14 (Third turn) - Miss - 81.25% probability to draw one of the cards I needed
11/13 (Fourth turn) - Miss - 87.5% probability to draw one of the cards I needed

How do I calculate the overall % of the 4 turns of not drawing 1 of the 11 cards I needed

In a row odds of 67.85%, Into 75%, Into 81.25%, Into 87.5%

Is it possible to calculate this?

 

[BigBeachBanana]

How do I calculate the overall % of the 4 turns of not drawing 1 of the 11 cards I needed

Yes, it's possible.
Not drawing 1 of the 11 winning cards is the same as drawing 1 of the 5 losing cards each turn.

Probability of drawing 1 of losing cards:
Turn 1: 5/16
Turn 2: 4/15
Turn 3: 3/14
Turn 4: 2/13

The answer is the product of 4 turns (5/16)*(4/15)*(3/14)*(2/13)= 1/364 which is approximately 0.275%.

 

[MarcSim88]

Yes, it's possible.
Not drawing 1 of the 11 winning cards is the same as drawing 1 of the 5 losing cards each turn.

Probability of drawing 1 of losing cards:
Turn 1: 5/16
Turn 2: 4/15
Turn 3: 3/14
Turn 4: 2/13

The answer is the product of 4 turns (5/16)*(4/15)*(3/14)*(2/13)= 1/364 which is approximately 0.275%.

Thankyou for the help, I always did like maths at school but didn't take it further than that.
Would you be able to briefly explain how the /364 is reached?

So I can better understand the equation and do it myself in the future

-Marc

 

[BigBeachBanana]

Thankyou for the help, I always did like maths at school but didn't take it further than that.
Would you be able to briefly explain how the /364 is reached?

So I can better understand the equation and do it myself in the future

-Marc

It came from reducing the fraction. If you want to see it yourself, multiply the fractions out yourself and reduce them.

 

[Steven G]

I would reduce the fractions first. If you reduced correctly, then the product of all the denominators will be 364

 

[MarcSim88]

It came from reducing the fraction. If you want to see it yourself, multiply the fractions out yourself and reduce them.

So it is essentially,

5 x 4 x 3 x 2 = 120
16 x 15 x 14 x 13 = 43,680

120/43680

120 divided by 43680 .......................................edited

Reduced to 1/364

Awesome, thankyou.