What is the Probability of Fibrillation After N Attempts?

[QuantumParadx]

Homework Statement

The question provides a table and asks:

Number of Attempts Fraction persisting in fibrillation
0 1.00
1 0.37
2 0.15
3 0.07
4 0.02

"Assume that the probability p of defibrillation on one attempt is independent of other attempts. Obtain an equation for the probability that the patient remains in fibrillation after N attempts. Compare it to the data and estimate p."

Homework Equations

Binomial Distribution

The Attempt at a Solution

I used the binomial distribution for my equation to estimate the probability that the patient remains in fibrillation. I'm not concerned about the "number of successes" in each attempt, so I believe this problem is similar to asking a coin toss question. For example, the probability that a coin will return heads after 1 attempt is 0.50. After 2 attempts, 0.5*0.5, etc.

Likewise, there are two possibilities: fibrillation and defibrillation. Instead of the coin example, the probability that the patient remains in fibrillation is 0.37. After two attempts, 0.37*0.37. After 3 attempts, 0.37*0.37*0.37, etc. It models the data rather well.

So then to estimate "p", the probability of defibrillation in each, p+q = 1 ---> p= 1-q

Does this sound reasonable?

 

[Andrew Mason]

Obtain an equation for the probability that the patient remains in fibrillation after N attempts. Compare it to the data and estimate p."

The Attempt at a Solution

I used the binomial distribution for my equation to estimate the probability that the patient remains in fibrillation. I'm not concerned about the "number of successes" in each attempt, so I believe this problem is similar to asking a coin toss question. For example, the probability that a coin will return heads after 1 attempt is 0.50. After 2 attempts, 0.5*0.5, etc.

Likewise, there are two possibilities: fibrillation and defibrillation. Instead of the coin example, the probability that the patient remains in fibrillation is 0.37. After two attempts, 0.37*0.37. After 3 attempts, 0.37*0.37*0.37, etc. It models the data rather well.

So then to estimate "p", the probability of defibrillation in each, p+q = 1 ---> p= 1-q

Does this sound reasonable?

The question asks for an equation. What is your equation for the probability that the patient remains in fibrillation after N attempts.

AM