4.2. Binomial Distributions http://www.ck12.org
n= 10
p=. 25
q=. 75
a= is the score being calculatedTABLE4.1:
X (Mark’s Score) Probability
0 10 C 0 ×. 250 ×. 7510 =. 056
1 10 C 1 ×. 251 ×. 759 =. 188
2 10 C 2 ×. 252 ×. 758 =. 282
3 10 C 3 ×. 253 ×. 757 =. 250
4 10 C 4 ×. 254 ×. 756 =. 146
5 10 C 5 ×. 255 ×. 755 =. 058
6 10 C 6 ×. 256 ×. 754 =. 016
7 10 C 7 ×. 257 ×. 753 =. 003
8 10 C 8 ×. 258 ×. 752 =. 000
9 10 C 9 ×. 259 ×. 751 =. 000
10 10 C 10 ×. 2510 ×. 750 =. 000Note: The probabilities for Mark scoring an 8, 9 or 10 are written as .000 because, while possible, each probability
is so small that when rounded to 3 decimal places it becomes 0.
Now we can plot a probability distribution and see that Mark is likely to get a few questions right, but he probably
will not pass.
The probability of Mark passing will beP(X= 6 )+P(X= 7 )+P(X= 8 )+P(X= 9 )+P(X= 10 ) =.019.
Guided Practice
A coin is tossed 5 times. Find the probability of getting exactly 3 heads.
Answer:
There are 5 trials, son=5.
A success is getting a head. We are interested in exactly 3 successes. Therefore,a=3.
The probability of a success is^12 , and, thus,p=^12.
Therefore, the probability of a failure is 1−^12 , or^12. From this, you know thatq=^12.