WEBVTT

1
00:00:00.000 --> 00:00:08.998
Here is the problem: X is binomial with n equals 8 and p equals 0.25. Find P(X less than or equal to 1).

2
00:00:09.448 --> 00:00:12.467
Binomial: k successes in n trials.

3
00:00:13.267 --> 00:00:16.982
Binomial probability of exactly j successes.

4
00:00:17.432 --> 00:00:20.125
Add the terms for j equals 0 to 1.

5
00:00:20.575 --> 00:00:23.431
Mean and standard deviation of the distribution.

6
00:00:24.231 --> 00:00:38.964
So the answer is P(X less than or equal to 1) approximately 0.3670806885 (36.708069 percent).

7
00:00:39.414 --> 00:00:49.422
With 8 independent trials and success probability 1 over 4 per trial, the requested probability is about 36.7081 percent.

8
00:00:50.222 --> 00:00:54.889
All binomial probabilities for j equals 0..8 add to 1.