00:01
Using the binomial formula, which is nx combinations, so n factorial over x factorial times n minus x factorial, that is being multiplied by our rate of success to the x power times our rate of failure to the n minus x power.
00:22
Now, we are given that n is equal to 4.
00:25
Our rate of success p is equal to 0 .15.
00:32
So our rate of failure is equal to 1 minus p will give us 0 .85.
00:41
Now, we want to find the probability that x is at most, so less than or equal to 1.
00:51
We also want to find the probability that x is at least so x is greater than or equal to three and finally the probability that x is less than one so for less than or equal to one this gives us the probability of x equals zero plus the probability of x equals one so when we use our equation for this will have 4 -0 combinations times 0 .15 to the 0th power times 0 .85 to the 4th power, plus 4 -1 combinations times 0 .15 to the 1 power times 0 .85 to the 3rd power.
02:01
X equals 0 will give us 0 .5211, and x equals 1 gives us 0 .36847.
02:28
So all we do, we just add those together and we get 0 .89048.
02:34
So the probability that x is less than or equal to 1 is 0 .89048.
02:46
Now for greater than or equal to 3, we only have the probability that x equals 3 plus the probability that x equals 4.
02:59
So again, setting up our equations, we have 43 combinations times 0 .15 to the 2 .5 to the, third power times 0 .85 to the first power plus for four combinations times 0 .15 to the fourth power times 0 .85 to the 0 .85 to the 0 .0.
03:33
Now, 4 4 combinations is just equal to 1...