probability of pulling consecutive numbers

[zerocool]

Imagine a theoretical game. Querying a random number generator which will pull a number from 0-99. Player wins if number drawn is 79 or less and loses if the number is 80-100. What is the probability of pulling a number that causes the player to lose (80-99) consecutively 1,2,3,4+ times. On one spin, the probability is I think 21/99 of losing but am confused how to calculate the probability of losing multiple times in a row.

 

[stapel]

Imagine a theoretical game. Querying a random number generator which will pull a number from 0-99. Player wins if number drawn is 79 or less and loses if the number is 80-100. What is the probability of pulling a number that causes the player to lose (80-99) consecutively 1,2,3,4+ times?

On one spin, the probability is I think 21/99 of losing but am confused how to calculate the probability of losing multiple times in a row.

How did you arrive at your value for losing on the first turn?

Please be complete. Thank you!

 

[JeffM]

Imagine a theoretical game. Querying a random number generator which will pull a number from 0-99. Player wins if number drawn is 79 or less and loses if the number is 80-100. What is the probability of pulling a number that causes the player to lose (80-99) consecutively 1,2,3,4+ times. On one spin, the probability is I think 21/99 of losing but am confused how to calculate the probability of losing multiple times in a row.

Are you familiar with binomial probabilities?

 

[HallsofIvy]

If A and B are "independent events", the probability of A happening is p, and the probability of B happening is q, then the probability of both A and B happening is p times q.

If the probability of event "A" happening is always p, irrespective of what happened before (so the trials are independent), then the probability of "A" happing twice is \(\displaystyle p^2\), three times in a row is \(\displaystyle p^3\), four times in a row is \(\displaystyle p^4\), etc.