http://www.ck12.org Chapter 4. Probability Distributions
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.
Obviously, you will be using technology to solve this problem, as it would take us a long time to calculate all of the
individual probabilities. The binomcdf function can be used as follows:
Therefore, the probability of havingat most30 heads from 50 tosses of a fair coin is 94.1%.
Guided Practice
A fair coin is tossed 50 times. What is the probability that you will get heads inat least30 of these tosses?
Answer:
There are 50 trials, son=50.
A success is getting a head, and we are interested inat least30 heads. Therefore,a= 50 , 49 , 48 , 47 , 46 , 45 , 44 , 43 , 42 , 41 , 40 , 39 , 38 , 37 , 36 , 35 , 34 , 33 , 32 , 31 ,
and 30.
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.
Again, you will obviously be using technology to solve this problem, as it would take us a long time to calculate all
of the individual probabilities. The binomcdf function can be used as follows:
Notice that when you use the phraseat least, you used the numbers 50, 0.5, 29. In other words, you would type in 1
−binomcdf(n,p,a− 1 ). Sincea=30, at leastawould be anything greater than 29. Therefore, the probability of
havingat least30 heads from 50 tosses of a fair coin is 10.1%.
Practice
- It is determined that because of a particular genetic trend in a family, the probability of having a boy is 60%.
Janet and David decide to have 4 children. What is the probability that Janet and David will have at least 2
boys?