Question

A doctor performs 8 operations in a given day. Assume that the operations are independent, and each operation is a success with probability 0.95. What’s the probability that the doctor has two or more failed operations on any given day? Calculate the exact binomial probabilities (do not use the normal approximation).

Answer 1

Let "S" be the probability of success on any one operation, which we know to be 0.95

The easiest way to do this is to calculate the probability of "0" failed operations and the probability of "1" failed operation, and subtract that sum from 1.

The probability of 0 failed operations is: (8C0)(S^8)(1 - S)^0

The probability of 1 failed operation is: (8C1)(S^7)(1 - S)^1

Make your substitutions, and do the subtraction.

Answer 2

All good now, @rupalpande ?

Answer 3

Ya got it

Answer 4

Good luck in all of your studies and thx for the recognition! @rupalpande

Answer 5

S=0.95 right?

Answer 6

whats is C0 and C1?

Answer 7

S is 0.95 There is no C0 or C1 by themselves. The full expressions are 8C0 and 8C1. "8 combination 0" and "8 combination 1".

Answer 8

"8 combination 0" and "8 combination 1" means?

Answer 9

I have not attended those class so not much clear abt it.

Answer 10

Here's a good short introduction to combinations and permutations. You really should read this to understand combinations which are key to understanding this problem. I could write out a whole explanation on it, but it would take up too much room, and you really need to know this. Otherwise, you won't be able to work the notation. You can skip down to where combinations are talked about.

http://mathforum.org/dr.math/faq/faq.comb.perm.html

Answer 11

Thanx

Answer 12

(8C0)(S^8)(1 - S)^0------- is the last power 0 is for whole term or just the for (1-s) term?

Answer 13

Just for the last factor.

Answer 14

ohhh....ok

Answer 15

Exponentiation takes precedence over multiplication, so it's the same as:

(8C0)(S^8)[(1 - S)^0]

but putting in the brackets is not necessary and just makes the whole thing look bulky and over-complicated.

Answer 16

thanx