Page 50 - Math SL HB Sem 3

) Finding the expected number (mean) of the binomial distribution
Given that x-B (n,p), the expected number of attempts to get a success would therefore be
n x p. Using the notation for probability distribution, the expectation of random variable, x:

E(x) - np

Similarly, the variance of the binomial distribution is defined asVar(x) np(t p)
= -
Hence, to answer parl (a) of the question that a fair die of six faces is thrown 10 times

\. solution:

a) That is, out of 10 attempts,
rrxr = ro ,1= I
6 3 """"'' one would expect to get a
3 about'7.7' times,

) Calculate the probability using the binomial distribution function

P(x=r)= (i)o't, p)n-"
-

where r = number of time6 obtaining a success,

(n\= ,.cr= ,n' .nandrEN
\r/ r! (n _ r)!

Hence, lo answer part (b) of the question that a fair die of six faces is thrown 10 times

\. solution:

b) The number of successes you want to find out is four, so r = 4
The probability of getting a '3' exactly four times is therefore:

10 t1
P(x=4): ( (a (:)"-'
+ ) )-

l0)
=( 4) H-H" The probability is rather
small, which is quite
:0,0543 sensible in reality.
GDC

f6 fin6 P(x = 4).

Calculator.T- ' DIST'tcall out 'binompdf (n, p ,r)' ;
Calculator-C- call out ' Binomial p.d.'
;
tEnter the upper limit, r (or'x'for Calculator-C) = 4, the number of trials ,
n =10, and the probability of success, p = 1 , accordingly.

lo