Page 51 - Math SL HB Sem 3
P. 51
Cumulative binomial probability :
To find the cumulative binomial probability, you need to first determine which probabilities are to
be summed up. For example,
P(x 3 2) - P(x = 0) + P(x t) + P(x = 2)
=
P(x<2)- P(x= 0)+P(x=1)
Note that the type of
the inequality sign P(x>2)= 1-P(x<1)
determines which
probahil ities should b e
: 1-
added- [P(x = 0) + P(x = 1)]
P(x>2)- r-P(x<2)
= 1 - P(x = 0) + P(x = r) + P(x - 2)l
Watch Out:
P(X = 0) may not be zero. Don't miss out this term!
GDC
Calculator-T-: 'DIST'- 'binomcdf (n, p ,0' ; Calculator-G- : call out 'Binomial c.d.'
E.g. To find
P(X < 2) t enter the upper limit, r (or 'x' for Calculalorc) = 2,,
the number of trails , n, and the probability of success, p, accordingly.
P(X > 2) ,gnter the upper limit , r (or'x'for Calculator-C) = 1,
the number of trails , n, and the probability of success, p, accordingly.
-
Then subtract the answer from 1. (i.e. 1 binomcdf (n,p ,r - l))
\. Example:
Amy tossed a fair coin eight times. Find the probability that she obtains
a) exactly 4 heads
b) at least 3 heads
\ sotution:
ldentify the values of n and
p first:
a) 1
x-B (8, There are B trials, so
2 n =8.
It is a fair coiL so
P(x=a)= p=P(head)=0.5
Always write down what 0()'()'-'
probability that you are
finding in the form of 7
P(x - x) =70 t6 x+)
35
(= 0.273)
t28
b) =1-P(x<2)
flx>:)
= - - = L) P(x = 2)
-
t P(x = 0) P(x
= ,- () (?)()'()'- ()'()"
Spot the word'at leas(, and H'(:)'- 0
form the prcbability 117
P(X > x). It is faster to do
256 32 64
-
1 P(X < 2) than to sum
219 P(x=3)+P(X=4)
256 +P(x=s)+P(x=6)
+P(x ='t) + P(x = B)
= 0.855Gon""t toz
"ie.tig:)
tl