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Taupānga Māori Probability Worksheet
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Taupānga Māori Probability Worksheet
🎲 Wāhanga 1: Ngā Pātai Kōwhiri Kotahi (Multiple Choice - Single Selection)
1. He aha te taupānga o te whakangaro i te mata kotahi i runga i te tapawhā rite? (What is the probability of rolling a 1 on a fair die?)
1/6
1/4
1/2
1/3
2. Mēnā he 20 kāri kei roto i te pouaka, ā he 5 whero, he aha te taupānga o te tango i tētahi kāri whero? (If there are 20 cards in a box and 5 are red, what's the probability of drawing a red card?)
1/4
1/5
5/20
1/3
3. He aha te taupānga mutunga rawa o tētahi tahunga? (What is the maximum probability of any event?)
0
0.5
1
100
4. Mēnā he 0.3 te taupānga o te ua āpōpō, he aha te taupānga kāore he ua? (If the probability of rain tomorrow is 0.3, what's the probability of no rain?)
0.3
0.7
0.6
1.3
5. He aha te taupānga o te whakangaro i te nama ōrite i runga i te tapawhā rite? (What's the probability of rolling an even number on a fair die?)
1/3
1/2
2/3
3/6
☑️ Wāhanga 2: Ngā Kōwhiringa Maha (Multiple Selection)
6. Kōwhiria ngā tahunga katoa e mutu ai (Select all events that are certain):
Ka eke te rā āpōpō
Ka whakangaro koe i te 7 i runga i te tapawhā
Ka ua āpōpō
Ka roa ake te rā i te pō
7. Kōwhiria ngā taupānga katoa e tika ana (Select all valid probabilities):
0.5
1.2
-0.3
3/4
0
8. Kōwhiria ngā tahunga katoa e kore ai e puta (Select all impossible events):
Whakangaro i te 8 i runga i te tapawhā rite
Tango i te kāri whero mai i te tapu kāri whero katoa
Ua i te rangi mārama
Whakangaro i te nama 1-6 i runga i te tapawhā rite
📝 Wāhanga 3: Ngā Whakakī Raina (Fill in the Blanks)
9. Mēnā he 50 tauira kei te akomanga, ā he 20 tama, he _______ te taupānga o te kōwhiri i tētahi tamāhine.
10. Te taupānga o ngā tahunga katoa e taea ana he _______.
11. Mēnā P(A) = 0.4, nā P(kāore a A) = _______.
12. I runga i te tapawhā rite, te taupānga o te whakangaro i te nama iti iho i te 4 he _______.
13. Mēnā he 100 kōura kei te moana, ā he 25 whero, te taupānga ōrau o te hopu i tētahi whero he _______.
14. Te taupānga o te whakangaro i te H i runga i te moni he _______.
15. Mēnā he 12 kāri kei te tapu, ā he 3 kīngi, te taupānga o te tango i tētahi kīngi he _______.
🔢 Wāhanga 4: Ngā Tatauranga Roa (Long Answer Problems)
16. Whakatauritehia te taupānga o te whakangaro i te nama nui ake i te 4 i runga i te tapawhā rite. Whakaatuhia tō mahi katoa.
17. He pouaka kei reira he 8 pōro whero, 6 kōwhai, 4 kikorangi. Whakatauritehia te taupānga o te tango i tētahi pōro kōwhai.
18. Mēnā P(A) = 0.6 ā P(B) = 0.3, ā he tahunga motuhake rāua, kimihia P(A me B).
19. Whakaatuhia he taauira o tētahi tahunga he 3/4 tōna taupānga.
20. Whakamāramahia te rerenga kē i waenga i ngā tahunga motuhake me ngā tahunga taupiri.
🎯 Wāhanga 5: Ngā Whakataurite Taupānga (Probability Calculations)
21. He roulette kei reira he 38 wāhi (18 whero, 18 mangu, 2 kākāriki). Whakatauritehia te taupānga o te whero.
22. Whakangaro koe i ngā tapawhā e rua. He aha te taupānga o te whakangaro i te tapeke 7?
23. Mēnā he 1000 tangata kei te tāone, ā he 450 wahine, whakatauritehia te taupānga o te hui i tētahi tāne.
24. He kete kei reira he 15 āporo (5 kino, 10 pai). Tangohia e rua, kāore he whakahoki. Whakatauritehia te taupānga he pai ngā mea e rua.
25. He aha te taupānga o te whakangaro i te nama kotahi, te rua, te toru rānei i runga i te tapawhā rite?
📊 Wāhanga 6: Ngā Ripanga Taupānga (Probability Tables)
26. Whakakīhia te ripanga nei mō te whakangaro i ngā tapawhā e rua:
Tapawhā 1 + Tapawhā 2 = Tapeke
P(tapeke = 2) = _______
P(tapeke = 7) = _______
P(tapeke = 12) = _______
P(tapeke ≤ 4) = _______
27. Whakaritehia tētahi ripanga taupānga mō te tango kāri mai i te tapu rite (52 kāri):
P(Kīngi) = _______
P(Kuīni) = _______
P(Ēhi) = _______
P(Kāri whero) = _______
P(Spades) = _______
🔄 Wāhanga 7: Ngā Tahunga Rōpū (Compound Events)
28. P(A) = 0.4, P(B) = 0.5, P(A ∩ B) = 0.2. Whakatauritehia P(A ∪ B).
29. Mēnā he tahunga motuhake a A me B, ā P(A) = 1/3, P(B) = 1/4, kimihia P(A me B).
30. He kāri e rua ka tangohia (me te whakahoki). Whakatauritehia te taupānga he whero ngā mea e rua.
31. Whakangaro koe i tētahi moni e toru ngā taima. He aha te taupānga o te whakangaro i ngā mata e toru?
32. P(kāore a A) = 0.3. He aha a P(A)?
🌳 Wāhanga 8: Ngā Rākau Taupānga (Probability Trees)
33. Waihangahia tētahi rākau taupānga mō te whakangaro i tētahi moni e rua ngā taima.
34. He pouaka A (3 whero, 2 kikorangi) me te pouaka B (1 whero, 4 kikorangi). Kōwhiri pouaka, kātahi tango kāri. Waihangahia te rākau taupānga.
35. Whakamahia tō rākau taupānga i te pātai 34 hei whakataurite i te taupānga o te tango i tētahi kāri whero.
🎲 Wāhanga 9: Ngā Tapawhā me ngā Moni (Dice and Coins)
36. Whakangaro koe i ngā tapawhā e rua. He aha te taupānga o te whakangaro i ngā nama ōrite?
1/6
1/12
1/36
6/36
37. Whakangaro koe i ngā moni e toru. Whakatauritehia te taupānga o te whakangaro i ngā mata e rua, kotahi whiore.
38. He tapawhā 8-mata. He aha te taupānga o te whakangaro i te nama nui ake i te 5?
39. Whakangaro koe i tētahi tapawhā, kātahi whakangaro i tētahi moni. He aha te taupānga o te whakangaro i te 6 me te mata?
40. He aha te taupānga o te whakangaro i te tapeke 11 mā ngā tapawhā e rua?
🃏 Wāhanga 10: Ngā Kāri (Cards)
41. Mai i te tapu kāri rite, he aha te taupānga o te tango i tētahi Jack o Hearts?
42. Tangohia ngā kāri e rua (kāore he whakahoki). Whakatauritehia te taupānga he Ēhi ngā mea e rua.
43. He aha te taupānga o te tango i tētahi kāri mata (Jack, Queen, King)?
3/52
12/52
4/52
1/13
44. Tangohia tētahi kāri, whakahokia, kātahi tangohia anō. He aha te taupānga he whero ngā mea e rua?
45. He aha te taupānga o te tango i tētahi kāri mangu rānei he mata rānei?
📈 Wāhanga 11: Ngā Taupānga Rōpū (Conditional Probability)
46. P(A|B) = 0.6, P(B) = 0.3. Whakatauritehia P(A ∩ B).
47. He 100 tauira: 60 wahine (20 pai ki te maths), 40 tāne (25 pai ki te maths). Kimihia P(pai ki te maths | wahine).
48. Mēnā he tahunga motuhake a A me B, he aha a P(A|B)?
P(A)
P(B)
0
1
49. P(A ∩ B) = 0.15, P(B) = 0.25. Whakatauritehia P(A|B).
50. Whakamāramahia te tikanga o te taupānga rōpū ki tō ake kupu.
🎪 Wāhanga 12: Ngā Taauira Taiao (Real World Examples)
51. He 80% te taupānga o te ua i te mutunga wiki. He aha te taupānga kāore he ua?
52. He kura kei reira he 500 ākonga. He 200 i te Tau 9, 150 i te Tau 10, 150 i te Tau 11. Mēnā ka kōwhiri ākonga kotahi, he aha te taupānga he Tau 10 ia?
53. He taupānga 1/1000 o te mate hōhā i ia tangata. I roto i te tāone 50,000 tangata, he tokomaha ka mate hōhā?
54. He kaiwhakamātau rongoa he 95% tōna tika. Mēnā he 1000 tangata ka whakamātauhia, tokomaha ka kitea he tika?
55. He taupānga 0.02 o te kino o ngā hua i te whare hoko. Mēnā ka hoko koe i ngā hua 50, he aha te taupānga he pai katoa?
🔍 Wāhanga 13: Ngā Whakataurite Uaua (Advanced Calculations)
56. He rōpū 12 tangata (5 wahine, 7 tāne). Kōwhiri e 3. He aha te taupānga he wahine katoa ngā mea e toru?
57. Whakangaro koe i tētahi tapawhā kia roa ai ka puta te 6. He aha te taupānga ka puta i te whakangaro tuatahi?
58. He pouaka kei reira he 10 pōro (6 whero, 4 kikorangi). Tangohia e 3 (kāore he whakahoki). Whakatauritehia te taupānga he whero katoa.
59. P(A ∪ B ∪ C) = ? mēnā he tahunga motuhake katoa, ā P(A) = 0.2, P(B) = 0.3, P(C) = 0.1?
60. He aha te taupānga o te whakangaro i te tapeke 8 mā ngā tapawhā e toru?
🎨 Wāhanga 14: Ngā Whakaaturanga (Visual Representations)
61. Whakaatuhia ki te kauwhata te taupānga o ia putanga mō te whakangaro tapawhā kotahi.
62. Waihangahia tētahi Venn diagram e whakaatu ai i ngā tahunga A me B mēnā P(A) = 0.4, P(B) = 0.3, P(A ∩ B) = 0.1.
63. Whakaatuhia ki te poraka kauwhata ngā taupānga o ngā tae i roto i te pouaka (30% whero, 25% kikorangi, 20% kōwhai, 25% kākāriki).
64. Waihangahia tētahi taupānga raina mō te whakangaro i ngā tapawhā e rua (tapeke 2-12).
🧮 Wāhanga 15: Ngā Tatauranga Tōkeke (Expected Value)
65. He kēmu: whakangaro tapawhā, whiwhi $2 mō te 6, ngaro $1 mō ngā mea katoa. He aha te uara tōkeke?
66. He roulette: $35 mō te nama tika, $0 mō ngā mea katoa. He aha te uara tōkeke mō te $1 tuku?
67. He taupānga 0.1 o te whiwhi $100, 0.9 o te whiwhi $0. He aha te uara tōkeke?
68. Whakamāramahia te tikanga o te uara tōkeke.
🔗 Wāhanga 16: Ngā Whakataurite Hononga (Matching Activities)
69. Whakahonogia ngā kupu ki ōna whakamārama:
1. Taupānga
2. Tahunga
3. Putanga
4. Mokowā
A. Te katoa o ngā putanga
B. Tētahi hua o te whakamātau
C. Te inenga o te pea o te puta
D. Tētahi mea ka puta rānei kāore rānei
70. Whakahonogia ngā taupānga ki ōna whakamārama:
1. 0
2. 0.5
3. 1
4. 1/6
A. Tahunga mutu
B. Tahunga kore
C. Tapawhā rite - nama kotahi
D. Moni rite
📋 Wāhanga 17: Ngā Pātai Poto (Short Answer Questions)
71. He aha te rerenga kē i waenga i te taupānga me te statistics?
72. Whakaatuhia he taauira o tētahi tahunga motuhake.
73. He aha ai he taupānga 0 tētahi tahunga?
74. Whakaatuhia he taauira o te taupānga rōpū i tō ao.
75. He aha te tikanga o "me te whakahoki" i ngā whakamātau?
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