http://www.ck12.org Chapter 4. Probability Distributions
The total probability for this example is calculated as follows:
P(X≤ 5 ) = 0. 201 + 0. 251 + 0. 215 + 0. 121 + 0. 0403 + 0. 00605
P(X≤ 5 ) = 0. 834
Therefore, the probability of seeing at most 5 people using a card in a random set of 10 people is 83.4%.
You can see now that the use of the TI-84 calculator can save a great deal of time when solving problems involving
the phrasesat least,more than,less than, orat most. This is due to the fact that the calculations become much more
cumbersome. You could have used the binomcdf function on the TI-84 calculator to solve Example A. Binomcdf
stands for binomial cumulative probability.
The key sequence for using the binompdf function is as follows:
If you used the data from Example A, you would find the following:
You can see how using the binomcdf function is a lot easier than actually calculating 6 probabilities and adding them
up. If you were to round 0.8337613824 to 3 decimal places, you would get 0.834, which is our calculated value
found in Example A.
Example B
Karen and Danny want to have 5 children after they get married. What is the probability that they will haveless than
3 girls?
There are 5 trials, son=5.
A success is when a girl is born, and we are interested inless than3 girls. Therefore,a= 2 , 1 ,and 0.
The probability of a success is 50%, or 0.50, and, thus,p= 0 .50.
Therefore, the probability of a failure is 1− 0 .50, or 0.50. From this, you know thatq= 0 .50.