8.2 Carraa Ta'uumsaa Ta'iilee Sasalphoo
1. Kaayyoo Barumsaa
- Foormulaa carraa ta'uumsaa ni baru.
- Ta'iilee sasalphoo (saantii, daayisii, fi kaardii) irratti herrega ni hojjetu.
- Bu'aa carraa bifa fraakshinii, deesimaalii, ykn dhibbeentaan (%) ni ibsu.
2. Yaadannoo (Key Notes)
Foormulaan Carraa Ta'uumsaa Ta'iinsa (E) tokkoo:
P(E) =
Baay'ina bu'aa ta'iinsichaa [n(E)]Baay'ina bu'aa samudaa [n(S)]
- n(E): Baay'ina carraawwan siif mijatan (favorable outcomes).
- n(S): Baay'ina bu'aawwan danda'aman hunda (total outcomes).
- Carraan ta'uumsaa hundi ida'amee 1 kenna.
3. Fakkeenyota (Examples)
1. Daayisii tokko darbuu keessatti carraan lakkoofsa 4 argachuu meeqa?
Deebii: n(E)=1, n(S)=6. P(E) =
Deebii: n(E)=1, n(S)=6. P(E) =
16
.2. Saantii tokko darbuu keessatti carraan Gubbaa (Head) argachuu meeqa?
Deebii: n(E)=1, n(S)=2. P(E) =
Deebii: n(E)=1, n(S)=2. P(E) =
12
(ykn 0.5).3. Saanduqa bifa burtukaanaa 3 fi bifa cuquliisaa 7 qabu keessaa tokko yoo fudhatame, carraan burtukaana ta'uu meeqa?
Deebii: n(S)=3+7=10. P(E) =
Deebii: n(S)=3+7=10. P(E) =
310
.4. Daayisii irratti carraan lakkoofsa 6 ol argachuu meeqa?
Deebii: n(E)=0. P(E) =
Deebii: n(E)=0. P(E) =
06
= 0.5. Carraan lakkoofsa parayimii (prime number) daayisii irratti argachuu meeqa?
Deebii: E = {2, 3, 5} → n(E)=3. P(E) =
Deebii: E = {2, 3, 5} → n(E)=3. P(E) =
36
= 1/2.4. Gaaffilee Shaakalaafi Ibsa (15)
1. Foormulaan P(E) maali?
Deebii: n(E) / n(S)Ibsa: Bu'aa barbaadamu baay'ina samudaatti hiruudha.
2. Daayisii irratti carraan lakkoofsa 'even' (2,4,6) argachuu meeqa?
Deebii: 1/2Ibsa: 3 / 6 = 1/2.
3. Saantii darbuu keessatti carraan Jala (Tail) argachuu meeqa?
Deebii: 0.5Ibsa: 1 / 2 = 0.5.
4. Boorsaa keessa kubbaa diimaa 5 fi adii 5 yoo jiraate, carraan diimaa fudhachuu meeqa?
Deebii: 1/2Ibsa: 5 / 10 = 1/2.
5. Carraan 'impossible event' meeqa?
Deebii: 0Ibsa: Ta'iinsi sun dhalachuu hin danda'u.
6. Carraan 'certain event' meeqa?
Deebii: 1Ibsa: %100 ni dhalata jechuudha.
7. Daayisii irratti carraan lakkoofsa 1 argachuu meeqa?
Deebii: 1/6Ibsa: n(E)=1, n(S)=6.
8. Saantii lama yoo darban, carraan lamaan isaanii gubbaa (HH) ta'uu meeqa?
Deebii: 1/4Ibsa: Samuda keessaa {HH, HT, TH, TT} keessaa 1/4.
9. Carraan lakkoofsa 10 gadii daayisii irratti argachuu meeqa?
Deebii: 1Ibsa: Lakkoofsonni hundi (1-6) 10 gadi waan ta'aniif (6/6=1).
10. Guyyoota torban keessaa carraan 'Wiixata' fudhachuu meeqa?
Deebii: 1/7Ibsa: n(S)=7, n(E)=1.
11. Carraan %25 ta'e herreegaan meeqa?
Deebii: 0.25 (ykn 1/4)Ibsa: 25 / 100 = 0.25.
12. Yoo carraan roobaa 0.7 ta'e, carraan roobuu dhabuu meeqa?
Deebii: 0.3Ibsa: 1 - 0.7 = 0.3.
13. Daayisii irratti carraan lakkoofsa 3 ykn 5 argachuu meeqa?
Deebii: 1/3Ibsa: 2 / 6 = 1/3.
14. Qalamni 3 adii fi 2 gurraacha yoo jiraate, carraan gurraacha fudhachuu meeqa?
Deebii: 2/5Ibsa: n(E)=2, n(S)=5.
15. 'n(S)' maal agarsiisa?
Deebii: Baay'ina bu'aawwan samudaa hundaIbsa: Total number of outcomes.