http://www.ck12.org Chapter 4. Probability Distributions
The probability of a success is 40%, or 0.40, and, thus,p= 0 .40.
Therefore, the probability of a failure is 1− 0 .40, or 0.60. From this, you know thatq= 0 .60.
P(X=a) =nCa×pa×q(n−a)
P(5 people using a card) = 10 C 5 ×p^5 ×q^5
P(5 people using a card) = 10 C 5 ×( 0. 40 )^5 ×( 0. 60 )^5
P(5 people using a card) = 252 × 0. 01024 × 0. 07776
P(5 people using a card) = 0. 201Therefore, the probability of seeing 5 people using a card in a random set of 10 people is 20.1%.
You could have also used technology to solve this problem, rather than pencil and paper calculations. However, with
technology, it is often very helpful to check our answers using pencil and paper as well. With Example A, you could
have used the binompdf function on the TI-84 calculator. Binompdf simply stands for binomial 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:
Notice that you typed in binompdf(n,p,a)to solve the problem.
Example B
Karen and Danny want to have 5 children after they get married. What is the probability that they will have exactly
3 girls?
There are 5 trials, son=5.
A success is when a girl is born, and we are interested in 3 girls. Therefore,a=3.
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.