Question

Use the binomial probability

distribution below to find the
probability that the number of successes is at most five.
x P(x)
00.000
10.004
2 0.033
3 3 0.132
40.297
50.356
6 0.178

Answer 1

Answer: 0.822

===================================================

Method 1

Add up the P(x) values from x = 0 to x = 5

0.000+0.004+0.033+0.132+0.297+0.356 = 0.822

-----------------------------------------

Method 2

If A and B are complementary events, then P(A)+P(B) = 1 and that leads to P(B) = 1-P(A).

We can think of the events defined as follows

• A = event of getting at most 5 (ie 5 or less)
• B = event of getting 6

Either A or B must happen, but not both simultaneously

P(B) = 0.178 from the table

P(A) = 1-P(B)

P(A) = 1-0.178

P(A) = 0.822

which is a shortcut compared to method 1. It's a much faster shortcut the larger the table is.