4.3. Binompdf Function http://www.ck12.org
P(X=a) =nCa×pa×q(n−a)
P(3 girls) = 5 C 3 ×p^3 ×q^2
P(3 girls) = 5 C 3 ×( 0. 50 )^3 ×( 0. 50 )^2
P(3 girls) = 10 × 0. 125 × 0. 25
P(3 girls) = 0. 3125Therefore, the probability of havingexactly3 girls from the 5 children is 31.25%.
When using technology, you will select the binompdf function, because you are looking for the probability ofexactly
3 girls from the 5 children.
Using the TI-84 calculator gave us the same result as our calculation (and was a great deal quicker).
Example C
A fair coin is tossed 50 times. What is the probability that you will get heads in 30 of these tosses?
There are 50 trials, son=50.
A success is getting a head, and we are interested inexactly30 heads. Therefore,a=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.
P(X=a) =nCa×pa×q(n−a)
P(30 heads) = 50 C 30 ×p^30 ×q^20
P(30 heads) = 50 C 30 ×( 0. 50 )^30 ×( 0. 50 )^20
P(30 heads) = ( 4. 713 × 1013 )×( 9. 313 × 10 −^10 )×( 9. 537 × 10 −^7 )
P(30 heads) = 0. 0419Therefore, the probability of gettingexactly30 heads from 50 tosses of a fair coin is 4.2%.
Using technology to check, you get the following: