1. The document contains examples and explanations of concepts related to probability, including sample spaces, events, fundamental probability rules, binomial distribution, and normal distribution. 2. Formulas are provided for calculating probabilities of events, union and intersection of events, binomial probabilities, and normal distribution probabilities. 3. Examples are worked out applying these concepts and formulas to calculate various probabilities like the probability of getting more than 2 successes in 5 trials with probability of success p = 0.4.

2. 1 8 2
S = {()A 2 3 4 5 6 7 8 9 IO J K Q
(‘A 2 3 4 5 6 7 8 9 10 J K Q
f@A2345678910JKQ
9 A2345678910JKQ)
SC 101

3. 5 . sample space uamlsTw!nLC 2 !n ia
S = {II 12 13 14 15 1 6
21 22 23 24 25 26
37 32 33 34 35 36
41 42 43 44 45 46
51 52 53 54 55 56
61 62 63 64 65 661
6 . Sample s p a c e uow”luxmCGEitl=it%ti Tws r777m7kTxhi”niud~
MizlU 1 %J ;a
S zz IO, 1, 2, 3, . . . . . 1
SC 101 1 8 3

4. .:,Y
exclusive event UUWI
1 8 4 SC 101

5. SC 101 1 8 5

6. +iXlfh 5.2
9,
3
= 3! = 3~2x1 = 6 ;g
via no = n!
I (n-r)!
'iz
1 8 6 SC 101

7. fix1d1~ 5-6 c&mu 2 flu T!-~nRU~JMw 5 nw!~~~~vilf%
5
c* =
5! 5!
(5-2)!2! =
=
.3! 2!
10 5;
SC 101 1 8 7

8. 1 8 8 SC 101

9. 1
SC 101 1 8 9

10. s = tq A2345678910JKQ
4, A234567891QJKQ
OA2345678910JKQ
VA234567891QJKQ]
1 9 0
P
1
. . =
1 52
SC 101

11. :. Pi =
a
n(A)
P(A) = -~
n(S)
fh ~341 P(A)
s = {HH, H T , T H , TTI
SC 101 1 9 1

12. s zz {ll, 1 2 , . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
6 1 , 62, ._..... 66)
~o?U-JUWO&'d6?U A = 7Co X 5C3
7! 5!
=
7!0! x 2!3!
= 1X5X2 = 10
P(A)
1 0 1
= -~
. . =220 22
1 9 2 SC 101

13. SC 101 1 9 3

14. 5.3 ngn?l~l9~~9u~~~~nYU(Fundamental Probability Rules)
S = {H, Ti
:* P(S) = P(H) + P(T) = ; + ; = !
A = {II, 22, 33, 44, 55, 661
:. P(A) = 2
5
.-. P(A) = 1 - P(A)
1 9 4 SC 101

15. events 1 S:l;a'l
P(A U B) = P(A) + P(B',
"na P(A UB)
:. P(AUB)= P(A) + P(B)
4 4 8=
5 2 +x- = 5 2
i
nJ$ 5 cl A LLR: B L$uLM?n?dm?
P(A II B) = P(A) + P(B) - P(A f-l B)
s = IHH, HT, TH, TTI
A = IHH, TT}
B = {HH, HT, TH}
SC 101 1 9 5

16. P(A) = $
P(B) = ;
. . AfIB = {HHI
P(A n B) = ;
:. P(A U B) = P(A) + P(B) - P(AnB)
2+--13=
4 4 4
4= jy =I = P(S) 1. AUU= s
s = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
1 9 6 SC 101

17. 5.4.1 nl5LLilnLLQQLUJUM~Ulu (Binomial distribution) ihnl~LL?nLL~3Ja~
SC 101 1 9 7

18. 1 9 8
. . P[X=31 =
=
5 x 2 10
=
8x4 = -32
SC 101

19. . . P[X>21= P[X = 2 1 + P[X=31 + P[X=4] + P[X=51
= 10 10 5 1
q+p+=+z =
2 6
3-F
M~Dal~~~Ml~l~~
P[X>21 = 1 - P[X_<ll i?G
LiEI P[X<ll z= P[X-01 + P[X=ll
1TZ 5-+- = 6
32 32 12
SC 101 199

20. :_ P[X>21 = 1 - $
2 6
=
37
= P[X=O] + P[X=ll + P[X=21 + P[X=31
1 5 10 10 2 6=
=+-+32+x = 3 2
= P[X=31 + P[X=41
10 5 15
=
=+27 = 32
l
2 0 0
.
SC 101

21. SC 101 2 0 1

22. . . q = 1 - P = 1-2 =
2
n = 180
. . i11a&l = np = 180x-- = 3 0
;
d3ulThJluuaJlFl5~lu = e = j-g
P[X=xl =
1
A-ii ./
x-p 2
; L - - l- -
u
2 0 2 SC 101

23. Y
x PI
SC 101

24. 2 0 4 SC ,101

25. 1 z2
P[Z=ZJ =‘- e-7 -
?a
a,< zi+M

26. bm~5vii P[73 < x < 7 5 . 5 1
9in X . 7 3 - 6 8=
1
73
. .
z z zz
1 2 . 5
2
x2 = 75.5 :. z2 =
7 5 . 5 - 6 8
-m- = 3
- P[73 < x < 75.51. . = PL2 < z < 31
PlZ i 31 - PiZ & 21
= 0.9987 - 0.9772
= 0.0215
2 0 6 SC 101

27. SC 101 2 0 7

28. n. P(AUB)
2 0 8 SC 101

29. SC 101 2 0 9

30. n. PIX <107.51
2 1 0 SC 101