�ݺ�ߣ

‫ﻣﻦ‬‫ﻣﻜﻮﻧﺔ‬‫ﺟﺒﻦ‬‫ﻓﻄﻴﺮﺓ‬‫ﺍﻟﻤﺠﺎﻭﺭ‬‫ﺍﻟﺸﻜﻞ‬‫ﻳﻤﺜﻞ‬
:‫ﻳﺄﺗﻲ‬‫ﻋﻤﺎ‬‫ﺍﻹﺟﺎﺑﺔ‬‫ﻓﻲ‬‫ﺑﺎﻟﺸﻜﻞ‬‫ﺍﺳﺘﻌﻦ‬.‫ﻣﺨﺘﻠﻔﺔ‬‫ﺃﻧﻮﺍﻉ‬‫ﺃﺭﺑﻌﺔ‬
‫ﺍﻟﻔﻄﻴﺮﺓ؟‬ ‫ﻓﻲ‬ ‫ﺍﻟﺸﻮﻛﻮﻻﺗﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻳﺪﻝ‬ ‫ﺍﻟﺬﻱ‬ ‫ﺍﻟﻜﺴﺮ‬ ‫ﻣﺎ‬‫ﺍﻟﻔﻄﻴﺮﺓ؟‬ ‫ﻓﻲ‬ ‫ﺍﻟﺸﻮﻛﻮﻻﺗﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻳﺪﻝ‬ ‫ﺍﻟﺬﻱ‬ ‫ﺍﻟﻜﺴﺮ‬ ‫ﻣﺎ‬‫ﺍﻟﻔﻄﻴﺮﺓ؟‬ ‫ﻓﻲ‬ ‫ﺍﻟﺸﻮﻛﻮﻻﺗﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻳﺪﻝ‬ ‫ﺍﻟﺬﻱ‬ ‫ﺍﻟﻜﺴﺮ‬ ‫ﻣﺎ‬‫ﺍﻟﻔﻄﻴﺮﺓ؟‬ ‫ﻓﻲ‬ ‫ﺍﻟﺸﻮﻛﻮﻻﺗﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻳﺪﻝ‬ ‫ﺍﻟﺬﻱ‬ ‫ﺍﻟﻜﺴﺮ‬ ‫ﻣﺎ‬ 
.‫ﺻﻮﺭﺓ‬ ‫ﺃﺑﺴﻂ‬ ‫ﻓﻲ‬ ‫ﺍﻛﺘﺒﻪ‬
،‫ﺗﺮﺍﻩ‬ ‫ﺃﻥ‬ ‫ﺩﻭﻥ‬ ‫ﹰ‬‫ﺎ‬‫ﻗﺴﻤ‬ ‫ﺃﻋﻄﺎﻙ‬ ‫ﺻﺪﻳﻘﻚ‬ ‫ﺃﻥ‬ ‫ﺍﻓﺮﺽ‬،‫ﺗﺮﺍﻩ‬ ‫ﺃﻥ‬ ‫ﺩﻭﻥ‬ ‫ﹰ‬‫ﺎ‬‫ﻗﺴﻤ‬ ‫ﺃﻋﻄﺎﻙ‬ ‫ﺻﺪﻳﻘﻚ‬ ‫ﺃﻥ‬ ‫ﺍﻓﺮﺽ‬،‫ﺗﺮﺍﻩ‬ ‫ﺃﻥ‬ ‫ﺩﻭﻥ‬ ‫ﹰ‬‫ﺎ‬‫ﻗﺴﻤ‬ ‫ﺃﻋﻄﺎﻙ‬ ‫ﺻﺪﻳﻘﻚ‬ ‫ﺃﻥ‬ ‫ﺍﻓﺮﺽ‬ 
‫ﻣﺴﺎﻭﻳﺔ‬ ‫ﺍﻟﺘﻮﺕ‬ ‫ﻓﻄﻴﺮﺓ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺤﺼﻮﻝ‬ ‫ﻓﺮﺻﺔ‬ ‫ﻓﻬﻞ‬
‫ﺍﻟﻔﺎﻧﻴﻼ؟‬ ‫ﻓﻄﻴﺮﺓ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺤﺼﻮﻝ‬ ‫ﻟﻔﺮﺻﺔ‬









‫ﺟﺒﻦ‬ ‫ﻓﻄﻴﺮﺓ‬
‫ﻋﺎﺩﻳﺔ‬‫ﺷﻮﻛﻮﻻﺗﺔ‬
‫ﺗﻮﺕ‬‫ﻓﺎﻧﻴﻼ‬
G7 SE MS Math 09
2nd pass
7-12-07
LKell
‫ﺍﻟﻔﻄﻴﺮﺓ؟‬ ‫ﻓﻲ‬ ‫ﺍﻟﺸﻮﻛﻮﻻﺗﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻳﺪﻝ‬ ‫ﺍﻟﺬﻱ‬ ‫ﺍﻟﻜﺴﺮ‬ ‫ﻣﺎ‬
C09-01A_NA_874046



‫ﺃﻭ‬ ‫ﻭﺍﺣﺪ‬ ‫ﻧﺎﺗﺞ‬ ‫ﻫﻲ‬ :‫ﻭﺍﻟﺤﺎﺩﺛﺔ‬ .‫ﺗﺠﺮﺑﺔﻣﺎ‬ ‫ﻣﻦ‬ ‫ﻳﻨﺘﺞ‬ ‫ﺃﻥ‬ ‫ﻳﻤﻜﻦ‬ ‫ﻣﺎ‬ ‫ﻛﻞ‬ ‫ﻫﻮ‬ : ‫ﺍﻟﻨﺎﺗﺞ‬
‫ﺃﻭ‬ ‫ﻓﺮﺻﺔ‬ ‫ﻭﺗﺴﻤﻰ‬ .‫ﺣﺎﺩﺛﺔ‬ ‫ﻫﻲ‬ ‫ﺍﻟﻌﺎﺩﻳﺔ‬ ‫ﺍﻟﻔﻄﻴﺮﺓ‬ ‫ﻗﻄﻌﺔ‬ ‫ﻋﻠﻰ‬ ‫ﻓﺎﻟﺤﺼﻮﻝ‬ .‫ﻧﻮﺍﺗﺞ‬ ‫ﻣﺠﻤﻮﻋﺔ‬
. ‫ﺍﻟﺤﺎﺩﺛﺔ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﺍﻟﺤﺎﺩﺛﺔ‬ ‫ﻭﻗﻮﻉ‬ ‫ﺇﻣﻜﺎﻧﻴﺔ‬

‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻓﺈﻥ‬ ، ‫ﻧﻔﺴﻬﺎ‬ ‫ﺍﻟﺤﺼﻮﻝ‬ ‫ﺇﻣﻜﺎﻧﻴﺔ‬ ‫ﻟﻬﺎ‬ ‫ﺍﻟﻨﻮﺍﺗﺞ‬ ‫ﻛﺎﻧﺖ‬ ‫ﺇﺫﺍ‬ 
‫ﺍﻟﻜﻠﻲ‬ ‫ﺍﻟﻌﺪﺩ‬ ‫ﺇﻟﻰ‬ ‫ﺍﻟﺤﺎﺩﺛﺔ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻨﻮﺍﺗﺞ‬ ‫ﻋﺪﺩ‬ ‫ﻧﺴﺒﺔ‬ ‫ﻫﻲ‬ ،‫ﺣﺎﺩﺛﺔ‬
. ‫ﺍﻟﻤﻤﻜﻨﺔ‬ ‫ﻟﻠﻨﻮﺍﺗﺞ‬
= ( ‫ﺣﺎﺩﺛﺔ‬ )‫ﺡ‬
‫ﺍﻟﺤﺎﺩﺛﺔ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻨﻮﺍﺗﺞ‬ ‫ﻋﺪﺩ‬
‫ﺍﻟﻜﻠﻲ‬ ‫ﺍﻟﻨﻮﺍﺗﺞ‬ ‫ﻋﺪﺩ‬
٦-١ ‫ﻣﻦ‬ ‫ﺑﺎﻷﻋﺪﺍﺩ‬ ‫ﻣﺮﻗﻢ‬ ‫ﻣﻜﻌﺐ‬ ‫ﺭﻣﻲ‬ ‫ﻋﻨﺪ‬ ‫ﺯﻭﺟﻲ‬ ‫ﻋﺪﺩ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺤﺼﻮﻝ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻣﺎ‬
‫ﻭﺍﺣﺪﺓ؟‬ ‫ﻣﺮﺓ‬
= ( ‫ﺯﻭﺟﻲ‬ ‫ﻋﺪﺩ‬ )‫ﺡ‬
‫ﺍﻟﻤﻤﻜﻨﺔ‬ ‫ﺍﻟﺰﻭﺟﻴﺔ‬ ‫ﺍﻷﻋﺪﺍﺩ‬ ‫ﻋﺪﺩ‬
‫ﻟﻠﻨﻮﺍﺗﺞ‬ ‫ﺍﻟﻜﻠﻲ‬ ‫ﺍﻟﻌﺪﺩ‬
=١
٢ = ٣
٦
. % ٥٠ ‫ﺃﻭ‬ ٠٫٥ ‫ﺃﻭ‬ ١
٢ ‫ﻫﻮ‬ ‫ﺯﻭﺟﻲ‬ ‫ﻋﺪﺩ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺤﺼﻮﻝ‬ ‫ﻓﺎﺣﺘﻤﺎﻝ‬
: ‫ﺻﻮﺭﺓ‬ ‫ﺑﺄﺑﺴﻂ‬ ‫ﻭﺍﻛﺘﺒﻬﺎ‬ ،‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻻﺣﺘﻤﺎﻻﺕ‬ ‫ﺃﻭﺟﺪ‬ ،‫ﺍﻟﺴﺎﺑﻖ‬ ‫ﺍﻟﻤﻜﻌﺐ‬ ‫ﺭﻣﻲ‬ ‫ﻋﻨﺪ‬
( ‫ﺃﻭﻟﻲ‬ ‫ﻋﺪﺩ‬ )‫ﺡ‬ (‫ﺝ‬ ( ٦ ‫ﺃﻭ‬ ٥ )‫ﺡ‬ (‫ﺏ‬ ( ‫ﻓﺮﺩﻱ‬ ‫ﻋﺪﺩ‬ )‫ﺡ‬ (‫ﺃ‬

‫ﻣﻦ‬ ‫ﺑﺎﻷﻋﺪﺍﺩ‬ ‫ﻣﺮﻗﻢ‬ ‫ﻣﻜﻌﺐ‬ ‫ﺭﻣﻲ‬ ‫ﻋﻨﺪ‬ ‫ﺯﻭﺟﻲ‬ ‫ﻋﺪﺩ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﺤﺼﻮﻝ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻣﺎ‬





C09-002C_829633



C09-002C_829633




 

‫ﺭﻣﻲ‬ ‫ﻋﻨﺪ‬ ،‫ﹰ‬‫ﻼ‬‫ﻓﻤﺜ‬ .‫ﻣﺼﺎﺩﻓﺔ‬ ‫ﻣﻨﻬﺎ‬ ‫ﻧﺎﺗﺞ‬ ‫ﻛﻞ‬ ‫ﺣﺪﺙ‬ ‫ﺇﺫﺍ‬ ‫ﺎ‬‫ﹼﹰ‬‫ﻴ‬‫ﻋﺸﻮﺍﺋ‬ ‫ﺗﺤﺪﺙ‬ ‫ﺍﻟﻨﻮﺍﺗﺞ‬ ‫ﺇﻥ‬ ‫ﻧﻘﻮﻝ‬
. ‫ﺎ‬‫ﹼﹰ‬‫ﻴ‬‫ﻋﺸﻮﺍﺋ‬ ‫ﺗﺤﺪﺙ‬ ‫ﻓﺎﻟﻨﻮﺍﺗﺞ‬ ،‫ﺍﻟﻤﺮﻗﻢ‬ ‫ﺍﻟﻤﻜﻌﺐ‬
‫ﻧﻬﺎﻳﺔ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻤﺪﺭﺳﺔ‬ ‫ﺣﻔﻞ‬ ‫ﺗﻨﻈﻴﻢ‬ ‫ﺍﻟﺜﻼﺛﺔ‬ ‫ﻭﺃﺻﺪﻗﺎﺅﻩ‬ ‫ﺃﺣﻤﺪ‬ ‫ﻳﻌﺘﺰﻡ‬ 
‫ﻋﺪﺩ‬ ‫ﺃﺻﻐﺮ‬ ‫ﻋﻠﻰ‬ ‫ﻳﺤﺼﻞ‬ ‫ﻣﻦ‬ ‫ﻫﻮ‬ ‫ﺍﻟﺤﻔﻞ‬ ‫ﻓﻘﺮﺍﺕ‬ ‫ﺪﻡ‬‫ﹼ‬‫ﻘ‬‫ﻳ‬ ‫ﻣﻦ‬ ‫ﺃﻥ‬ ‫ﻋﻠﻰ‬ ‫ﺍﺗﻔﻘﻮﺍ‬ ،‫ﺍﻟﻌﺎﻡ‬
.٢ ، ٥ ،٦ ‫ﺍﻷﻋﺪﺍﺩ‬ ‫ﻋﻠﻰ‬ ‫ﺃﺣﻤﺪ‬ ‫ﺃﺻﺪﻗﺎﺀ‬ ‫ﺣﺼﻞ‬ ‫ﺇﺫﺍ‬ .‫ﺍﻟﻤﺮﻗﻢ‬ ‫ﺍﻟﻤﻜﻌﺐ‬ ‫ﻋﻠﻰ‬ ‫ﻳﻈﻬﺮ‬
‫ﺍﻟﺤﻔﻞ؟‬ ‫ﻓﻘﺮﺍﺕ‬ ‫ﺃﺣﻤﺪ‬ ‫ﺪﻡ‬‫ﹼ‬‫ﻘ‬‫ﻳ‬ ‫ﺃﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻓﻤﺎ‬
.٦ ، ٥ ، ٤ ، ٣ ، ٢ ، ١ :‫ﻫﻲ‬ ،‫ﺍﻟﻤﺮﻗﻢ‬ ‫ﺍﻟﻤﻜﻌﺐ‬ ‫ﺭﻣﻲ‬ ‫ﻧﻮﺍﺗﺞ‬ ‫ﹼ‬‫ﺇﻥ‬
.١ ‫ﺍﻟﻌﺪﺩ‬ ‫ﻋﻠﻰ‬ ‫ﻳﺤﺼﻞ‬ ‫ﺃﻥ‬ ‫ﻋﻠﻴﻪ‬ ‫ﺍﻟﺤﻔﻞ‬ ‫ﻓﻘﺮﺍﺕ‬ ‫ﺃﺣﻤﺪ‬ ‫ﻳﻘﺪﻡ‬ ‫ﻭﻟﻜﻲ‬
.‫ﺍﻟﺤﻔﻞ‬ ‫ﻓﻘﺮﺍﺕ‬ ‫ﺃﺣﻤﺪ‬ ‫ﻳﻘﺪﻡ‬ ‫ﺃﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻫﻮ‬ ( ‫ﺍ‬ )‫ﺡ‬ ‫ﻟﻴﻜﻦ‬
= (‫ﺍ‬)‫ﺡ‬
‫ﺍﻟﺤﻔﻞ‬ ‫ﻓﻘﺮﺍﺕ‬ ‫ﻳﻘﺪﻡ‬ ‫ﺃﺣﻤﺪ‬ ‫ﺗﺠﻌﻞ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻨﻮﺍﺗﺞ‬ ‫ﻋﺪﺩ‬
‫ﺍﻟﻜﻠﻲ‬ ‫ﺍﻟﻨﻮﺍﺗﺞ‬ ‫ﻋﺪﺩ‬
=١
٦
.% ١٧ ‫ﺣﻮﺍﻟﻲ‬ ‫ﺃﻭ‬ ،١
٦ ‫ﻫﻮ‬ ‫ﺍﻟﺤﻔﻞ‬ ‫ﻓﻘﺮﺍﺕ‬ ‫ﺃﺣﻤﺪ‬ ‫ﺪﻡ‬‫ﹼ‬‫ﻘ‬‫ﻳ‬ ‫ﺃﻥ‬ ‫ﻓﺎﺣﺘﻤﺎﻝ‬ ،‫ﻭﻋﻠﻴﻪ‬
‫ﻓﻲ‬ ‫ﻣﺒﻴﻦ‬ ‫ﻫﻮ‬ ‫ﻛﻤﺎ‬ ، ‫ﹰ‬‫ﺎ‬‫ﻣﻮﻇﻔ‬ ١٤ ‫ﺷﺮﻛﺔ‬ ‫ﻓﻲ‬ ‫ﻳﻌﻤﻞ‬ 
‫ﺎ‬‫ﹼﹰ‬‫ﻴ‬‫ﻋﺸﻮﺍﺋ‬ ‫ﺍﻟﻤﻮﻇﻔﻴﻦ‬ ‫ﺃﺣﺪ‬ ‫ﺍﻟﺸﺮﻛﺔ‬ ‫ﺍﺧﺘﺎﺭﺕ‬ ‫ﺇﺫﺍ‬ . ‫ﺍﻟﺠﺪﻭﻝ‬
،‫ﺍﻟﺸﺮﻛﺔ‬ ‫ﻧﻔﻘﺔ‬ ‫ﻋﻠﻰ‬ ‫ﺍﻟﻌﺎﻡ‬ ‫ﻟﻬﺬﺍ‬ ‫ﺍﻟﺤﺞ‬ ‫ﻓﺮﻳﻀﺔ‬ ‫ﻷﺩﺍﺀ‬
‫ﺑﺄﺑﺴﻂ‬ ‫ﻭﺍﻛﺘﺒﻬﺎ‬ ،‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻟﺤﻮﺍﺩﺙ‬ ‫ﺍﺣﺘﻤﺎﻻﺕ‬ ‫ﻓﺄﻭﺟﺪ‬
:‫ﺻﻮﺭﺓ‬
( ‫ﻣﻬﻨﺪﺱ‬ ‫ﺃﻭ‬ ‫ﺳﺎﺋﻖ‬ )‫ﺡ‬ (‫ﻫـ‬ ( ‫ﺳﺎﺋﻖ‬ )‫ﺡ‬ (‫ﺩ‬
( ‫ﺳﺎﺋﻖ‬ ‫ﺃﻭ‬ ‫ﻓﻨﻲ‬ )‫ﺡ‬ (‫ﺡ‬ ( ‫ﻃﺒﻴﺐ‬ )‫ﺡ‬ (‫ﺯ‬

‫ﺍﻟﻮﻇﻴﻔﺔ‬‫ﺍﻟﻌﺪﺩ‬
‫ﻣﺤﺎﺳﺐ‬٦
‫ﻓﻨﻲ‬٤
‫ﺳﺎﺋﻖ‬٣
‫ﻣﻬﻨﺪﺱ‬١
‫ﺃﻭ‬‫ﺍ‬ ‫ﹰ‬‫ﺻﻔﺮ‬‫ﻳﻜﻮﻥ‬‫ﻭﻗﺪ‬‫ﺍﻟﺼﺤﻴﺢ‬‫ﻭﺍﻟﻮﺍﺣﺪ‬‫ﺍﻟﺼﻔﺮ‬‫ﺑﻴﻦ‬‫ﻳﻘﻊ‬‫ﻋﺪﺩ‬‫ﻫﻮ‬‫ﻣﺎ‬‫ﺣﺎﺩﺙ‬‫ﻭﻗﻮﻉ‬‫ﺍﺣﺘﻤﺎﻝ‬
‫ﻛﻤﺎ‬،‫ﻧﺴﺒﺔ‬‫ﺃﻭ‬‫ﻋﺸﺮﻱ‬‫ﻛﺴﺮ‬‫ﺃﻭ‬‫ﺍﻋﺘﻴﺎﺩﻱ‬‫ﻛﻜﺴﺮ‬‫ﺍﻻﺣﺘﻤﺎﻝ‬‫ﻛﺘﺎﺑﺔ‬‫ﻳﻤﻜﻦ‬‫ﺃﻧﻪ‬‫ﻻﺣﻆ‬.‫ﺍ‬‫ﻭﺍﺣﺪﹰ‬
.‫ﺃﺩﻧﺎﻩ‬‫ﺍﻷﻋﺪﺍﺩ‬‫ﺧﻂ‬‫ﻋﻠﻰ‬‫ﻣﻮﺿﺢ‬‫ﻫﻮ‬
 


 
١
٤
٣
٤
١
٢












‫ﺍﻟﺤﺮﺍﻡ‬ ‫ﺍﻟﻠﻪ‬ ‫ﺑﻴﺖ‬ ‫ﺣﺠﺎﺝ‬ ‫ﻋﺪﺩ‬ ‫ﺑﻠﻎ‬
.‫٩٢٤١ﻫـ‬ ‫ﻋﺎﻡ‬ ‫ﺎ‬ ‫ﹰ‬‫ﺣﺎﺟ‬ ٢٤٠٨٨٤٩
 

‫ﺍﻟﺤﻔﻞ؟‬ ‫ﻓﻘﺮﺍﺕ‬ ‫ﺃﺣﻤﺪ‬ ‫ﺪﻡ‬‫ﹼ‬‫ﻘ‬‫ﻳ‬ ‫ﺃﻻ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻣﺎ‬ ، ٢ ‫ﻣﺜﺎﻝ‬ ‫ﻓﻲ‬ 
‫ﺃﺣﻤﺪ‬ ‫ﻡ‬‫ﻳﻘﺪﹼ‬ ‫ﺃﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻤﺔ‬‫ﹼ‬‫ﻣﺘﻤ‬ ‫ﻫﻮ‬ ،‫ﺍﻟﺤﻔﻞ‬ ‫ﻓﻘﺮﺍﺕ‬ ‫ﺃﺣﻤﺪ‬ ‫ﺪﻡ‬‫ﹼ‬‫ﻘ‬‫ﻳ‬ ‫ﺃﻻ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﺇﻥ‬
.‫ﺍﻟﺤﻔﻞ‬ ‫ﻓﻘﺮﺍﺕ‬
١ = ( ‫ﹶ‬‫ﺍ‬ )‫ﺡ‬ + ( ‫ﺍ‬ )‫ﺡ‬
١ = ( ‫ﹶ‬‫ﺍ‬ )‫ﺡ‬ + ١
٦
١
٦- ١
٦ -
٥
٦ = ( ‫ﹶ‬‫ﺍ‬ )‫ﺡ‬
.% ٨٣ ‫ﺣﻮﺍﻟﻲ‬ ‫ﺃﻭ‬ ، ٥
٦ ‫ﻫﻮ‬ ‫ﺍﻟﺤﻔﻞ‬ ‫ﻓﻘﺮﺍﺕ‬ ‫ﺃﺣﻤﺪ‬ ‫ﻡ‬‫ﻳﻘﺪﹼ‬ ‫ﺃﻻ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻓﺈﻥ‬ ،‫ﻭﻋﻠﻴﻪ‬
،‫ﻣﺠﻤﻮﻋﺎﺕ‬ ٦ ‫ﺇﻟﻰ‬ ‫ﺍﻟﻤﺘﻮﺳﻂ‬ ‫ﺍﻷﻭﻝ‬ ‫ﺍﻟﺼﻒ‬ ‫ﻃﻠﺒﺔ‬ ‫ﺑﺘﻮﺯﻳﻊ‬ ‫ﻣﻌﻠﻢ‬ ‫ﻗﺎﻡ‬ 
‫ﻓﻲ‬ ‫ﻛﻤﺎ‬ ‫ﹰ‬‫ﺍ‬‫ﺍﺭ‬‫ﹼ‬‫ﺩﻭ‬ ‫ﹰ‬‫ﺎ‬‫ﻗﺮﺻ‬ ‫ﺍﻟﻤﻌﻠﻢ‬ ‫ﺍﺳﺘﻌﻤﻞ‬ ‫ﺇﺫﺍ‬ . ‫ﻣﺎ‬ ‫ﺑﻨﺸﺎﻁ‬ ‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻛﻞ‬ ‫ﺗﻘﻮﻡ‬ ‫ﺃﻥ‬ ‫ﻋﻠﻰ‬
: ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻓﻤﺎ‬ ،‫ﻧﺸﺎﻃﺎﺗﻬﻢ‬ ‫ﻟﻌﺮﺽ‬ ‫ﺍﻟﻤﺠﻤﻮﻋﺎﺕ‬ ‫ﺗﺮﺗﻴﺐ‬ ‫ﻟﺘﺤﺪﻳﺪ‬ ‫ﺍﻟﺸﻜﻞ‬
‫؟‬ ‫ﹰ‬‫ﻻ‬‫ﺃﻭ‬ ‫ﻧﺸﺎﻃﻬﺎ‬ ‫ﺗﻌﺮﺽ‬ ‫ﻣﻦ‬ ‫ﻫﻲ‬ ‫ﺍﻟﺮﺍﺑﻌﺔ‬ ‫ﺍﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺃﻻ‬ (‫)ﺃ‬
‫ﺗﻌﺮﺽ‬ ‫ﻣﻦ‬ ‫ﻫﻲ‬ ‫ﺍﻟﺜﺎﻟﺜﺔ‬ ‫ﻭﻻ‬ ‫ﺍﻷﻭﻟﻰ‬ ‫ﺍﻟﻤﺠﻤﻮﻋﺔ‬ ‫ﺗﻜﻮﻥ‬ ‫ﺃﻻ‬ (‫)ﺏ‬
‫؟‬ ‫ﹰ‬‫ﻻ‬‫ﺃﻭ‬ ‫ﻧﺸﺎﻃﻬﺎ‬


‫ﻣﺜﺎﻝ‬ ‫ﻓﻲ‬  
:‫ﺻﻮﺭﺓ‬ ‫ﺑﺄﺑﺴﻂ‬ ‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻻﺣﺘﻤﺎﻻﺕ‬ ‫ﻹﻳﺠﺎﺩ‬ ‫ﺍﺭ‬‫ﹼ‬‫ﺍﻟﺪﻭ‬ ‫ﺍﻟﻘﺮﺹ‬ ‫ﺍﺳﺘﻌﻤﻞ‬
( ‫ﺔ‬‫ﹼ‬‫ﻠ‬‫ﻋ‬ ‫ﺣﺮﻑ‬ )‫ﺡ‬  ( ‫ﺭ‬ ‫ﺃﻭ‬ ‫ﻕ‬ )‫ﺡ‬  ( ‫ﻡ‬ )‫ﺡ‬ 
‫ﺛﻢ‬ ،‫ﺑﺮﺗﻘﺎﻟﻴﺔ‬ ‫ﻛﺮﺍﺕ‬ ٦‫ﻭ‬ ،‫ﺣﻤﺮﺍﺀ‬ ‫ﻛﺮﺓ‬ ١٢‫ﻭ‬ ،‫ﺳﻮﺩﺍﺀ‬ ‫ﻛﺮﺍﺕ‬ ٥‫ﻭ‬ ،‫ﺯﺭﻗﺎﺀ‬ ‫ﻛﺮﺍﺕ‬ ٧ ‫ﻛﻴﺲ‬ ‫ﻓﻲ‬ ‫ﻊ‬ ‫ﹺ‬‫ﻭﺿ‬
:‫ﺻﻮﺭﺓ‬ ‫ﺑﺄﺑﺴﻂ‬ ‫ﻭﺍﻛﺘﺒﻬﺎ‬ ،‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻻﺣﺘﻤﺎﻻﺕ‬ ‫ﺃﻭﺟﺪ‬ .‫ﻋﺸﻮﺍﺋﻲ‬ ‫ﺑﺸﻜﻞ‬ ‫ﺍﻟﻜﻴﺲ‬ ‫ﻣﻦ‬ ‫ﻛﺮﺓ‬ ‫ﺤﺒﺖ‬ ‫ﹸ‬‫ﺳ‬
( ‫ﺧﻀﺮﺍﺀ‬ )‫ﺡ‬  ( ‫ﺑﺮﺗﻘﺎﻟﻴﺔ‬ ‫ﺃﻭ‬ ‫ﺣﻤﺮﺍﺀ‬ )‫ﺡ‬  ( ‫ﺳﻮﺩﺍﺀ‬ )‫ﺡ‬ 
( ‫ﺻﻔﺮﺍﺀ‬ ‫ﻟﻴﺴﺖ‬ )‫ﺡ‬  ( ‫ﺑﺮﺗﻘﺎﻟﻴﺔ‬ ‫ﺃﻭ‬ ‫ﺣﻤﺮﺍﺀ‬ ‫ﻟﻴﺴﺖ‬ )‫ﺡ‬  ( ‫ﺯﺭﻗﺎﺀ‬ ‫ﻟﻴﺴﺖ‬ )‫ﺡ‬ 
‫ﺍﻷﻭﻝ‬ ‫ﺍﻟﺼﻒ‬ ‫ﻃﻼﺏ‬ ‫ﻗﺮﺃﻫﺎ‬ ‫ﺍﻟﺘﻲ‬ ‫ﺍﻟﻘﺼﺺ‬ ‫ﻋﺪﺩ‬ ‫ﺍﻟﺠﺪﻭﻝ‬ ‫ﻳﺒﻴﻦ‬ 
‫ﺃﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻓﻤﺎ‬ ، ‫ﺎ‬‫ﹼﹰ‬‫ﻴ‬‫ﻋﺸﻮﺍﺋ‬ ‫ﺍﻟﻄﻼﺏ‬ ‫ﺃﺣﺪ‬ ‫ﺍﺧﺘﺮﻧﺎ‬ ‫ﺇﺫﺍ‬ .‫ﺍﻟﻤﺘﻮﺳﻂ‬
‫؟‬ ‫ﺃﻛﺜﺮ‬ ‫ﺃﻭ‬ ‫ﻗﺼﺺ‬ ٣ ‫ﻗﺮﺃ‬ ‫ﻳﻜﻮﻥ‬



‫ﺔ‬‫ﹼ‬‫ﺍﻟﻤﺘﻤ‬ ‫ﺗﻌﺮﻳﻒ‬
١
٦
= (‫ﺍ‬ )‫ﺡ‬ ‫ﺿﻊ‬
‫ﻃﺮﻑ‬ ‫ﻛﻞ‬ ‫ﻣﻦ‬ ١
٦
‫ﺍﻃﺮﺡ‬
٥
٦
= ١
٦
- ٦
٦
= ١
٦
- ١
6
5 2
4 3
1
C10-002A_874046
ART FILE:
CUSTOMER:
CREATED BY:
EDITED BY:
JOB NUMBER:
DATE:
DATE:
TIME:
Glencoe
TECH
10555
C09-02A_NA_874046
6 m
6-19-07CS
Q h
¢S ¿
Ü¥
Ωää
C09-02A_NA_874046
‫ﺍﻟﻘﺼﺺ‬ ‫ﻋﺪﺩ‬‫ﺍﻟﻄﻼﺏ‬ ‫ﻋﺪﺩ‬
‫ﺻﻔﺮ‬٦
٢–١١٥
‫ﺃﻛﺜﺮ‬ ‫ﺃﻭ‬ ٣٤
 

 ‫ﺍ‬  ‫ﺍ‬ 
 ‫ﺍ‬ 

 ‫ﺍ‬  ‫ﺍ‬ 
 ‫ﺍ‬ – ‫ﺍ‬ 

‫ﺍ‬
‫ﻫﻤﺎ‬ ‫ﺍﻟﺤﺎﺩﺛﺘﺎﻥ‬ ‫ﻫﺎﺗﺎﻥ‬ . ‫ﻓﻴﻬﺎ‬ ‫ﻳﺸﺎﺭﻙ‬ ‫ﻻ‬ ‫ﺃﻭ‬ ‫ﺍﻟﻤﺪﺭﺳﻴﺔ‬ ‫ﺍﻟﺮﺣﻠﺔ‬ ‫ﻓﻲ‬ ‫ﺳﻠﻤﺎﻥ‬ ‫ﻳﺸﺎﺭﻙ‬ ‫ﻗﺪ‬
‫ﺃﻭ‬ ، ١ ‫ﻳﺴﺎﻭﻱ‬ ‫ﻣﺘﻤﻤﺘﻬﺎ‬ ‫ﻭﺍﺣﺘﻤﺎﻝ‬ ‫ﺍﻟﺤﺎﺩﺛﺔ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻣﺠﻤﻮﻉ‬ ‫ﺇﻥ‬ . ‫ﻣﺘﺘﺎﻣﺘﺎﻥ‬ ‫ﺣﺎﺩﺛﺘﺎﻥ‬
١ = ( ‫ﹶ‬‫ﺍ‬ )‫ﺡ‬ + ( ‫ﺍ‬ )‫ﺡ‬ : ‫ﺑﺎﻟﺮﻣﻮﺯ‬ ‫ﻭ‬ ،% ١٠٠
 

‫ﺍﻷﻣﺜﻠﺔ‬ ‫ﺍﻧﻈﺮ‬
١
٢
٣
‫ﻟﻠﺘﻤﺎﺭﻳﻦ‬
١٤-١١
٢٠-١٧
١٦،١٥
٢١،٢٢


‫ﻣﺠﻤﻮﻋﺔ‬ ‫ﻣﻦ‬ ‫ﺎ‬‫ﹼﹰ‬‫ﻴ‬‫ﻋﺸﻮﺍﺋ‬ ‫ﺑﻄﺎﻗﺔ‬ ‫ﺳﺤﺒﺖ‬ ‫ﺇﺫﺍ‬ ، ٢٠ ، ... ،٣ ، ٢ ،١ ‫ﺑﺎﻷﻋﺪﺍﺩ‬ ‫ﺑﻄﺎﻗﺔ‬ ٢٠ ‫ﻤﺖ‬‫ﹼ‬‫ﻗ‬‫ﹸﺭ‬
:‫ﺻﻮﺭﺓ‬ ‫ﺑﺄﺑﺴﻂ‬ ‫ﻭﺍﻛﺘﺒﻬﺎ‬ ،‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻻﺣﺘﻤﺎﻻﺕ‬ ‫ﻓﺄﻭﺟﺪ‬ ،‫ﺍﻟﻌﺸﺮﻳﻦ‬ ‫ﺍﻟﺒﻄﺎﻗﺎﺕ‬
( ٣ ‫ﺍﻟﻌﺪﺩ‬ ‫ﻣﻀﺎﻋﻔﺎﺕ‬ )‫ﺡ‬  ( ١٣ ‫ﺃﻭ‬ ٣ )‫ﺡ‬  ( ١ )‫ﺡ‬ 
( ١٠ ‫ﺍﻟﻌﺪﺩ‬ ‫ﻋﻮﺍﻣﻞ‬ ‫ﻣﻦ‬ ‫ﻟﻴﺲ‬ )‫ﺡ‬  ( ٢٠ ‫ﻟﻴﺲ‬ )‫ﺡ‬  ( ‫ﺯﻭﺟﻲ‬ ‫ﻋﺪﺩ‬ )‫ﺡ‬ 
‫ﻓﻲ‬ ‫ﺍﻟﻤﺴﺎﺑﻘﺎﺕ‬ ￯‫ﺇﺣﺪ‬ ‫ﻓﻲ‬ ‫ﺍﻟﻤﺸﺎﺭﻛﻴﻦ‬ ‫ﻋﺪﺩ‬ ‫ﺍﻟﺠﺪﻭﻝ‬ ‫ﻳﺒﻴﻦ‬ 
‫ﹰ‬‫ﺎ‬‫ﻋﺸﻮﺍﺋﻴ‬ ‫ﺍﻟﻤﺸﺎﺭﻛﻴﻦ‬ ‫ﺃﺣﺪ‬ ‫ﺍﺧﺘﻴﺎﺭ‬ ‫ﺗﻢ‬ ‫ﺃﻧﻪ‬ ‫ﺍﻓﺘﺮﺽ‬ .‫ﺍﻟﻤﻜﺮﻣﺔ‬ ‫ﻣﻜﺔ‬ ‫ﻣﻨﻄﻘﺔ‬
:‫ﺻﻮﺭﺓ‬ ‫ﺑﺄﺑﺴﻂ‬ ‫ﻭﺍﻛﺘﺒﻬﺎ‬ ،‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻻﺣﺘﻤﺎﻻﺕ‬ ‫ﻓﺄﻭﺟﺪ‬ ،‫ﺑﺎﻟﻤﺴﺎﺑﻘﺔ‬ ‫ﻟﻠﻔﻮﺯ‬
( ‫ﺍﻟﻄﺎﺋﻒ‬ ‫ﻣﺪﻳﻨﺔ‬ ‫ﻣﻦ‬ )‫ﺡ‬  ( ‫ﺃﻧﺜﻰ‬ )‫ﺡ‬ 
( ‫ﻣﻜﺔ‬ ‫ﻣﺪﻳﻨﺔ‬ ‫ﻣﻦ‬ )‫ﺡ‬  ( ‫ﺃﻧﺜﻰ‬ ‫ﺃﻭ‬ ‫ﺫﻛﺮ‬ )‫ﺡ‬ 
( ‫ﻣﻜﺔ‬ ‫ﻣﺪﻳﻨﺔ‬ ‫ﺃﻭ‬ ‫ﺍﻟﻄﺎﺋﻒ‬ ‫ﻣﺪﻳﻨﺔ‬ ‫ﻣﻦ‬ )‫ﺡ‬  ( ‫ﺍﻟﻄﺎﺋﻒ‬ ‫ﻣﺪﻳﻨﺔ‬ ‫ﻣﻦ‬ ‫ﻟﻴﺲ‬ )‫ﺡ‬ 
،‫ﺍﻷﺷﺠﺎﺭ‬ ￯‫ﺇﺣﺪ‬ ‫ﻇﻞ‬ ‫ﻓﻲ‬ ‫ﻃﻔﻞ‬ ‫ﺟﻠﺲ‬ ‫ﺇﺫﺍ‬ .‫ﺗﻔﺎﺡ‬ ‫ﺷﺠﺮﺍﺕ‬ ٨ ‫ﺑﻴﻨﻬﺎ‬ ‫ﻣﻦ‬ ،‫ﺷﺠﺮﺓ‬ ٧٥ ‫ﺑﺴﺘﺎﻥ‬ ‫ﻓﻲ‬ 
.‫ﺻﻮﺭﺓ‬ ‫ﺑﺄﺑﺴﻂ‬ ‫ﺇﺟﺎﺑﺘﻚ‬ ‫ﺍﻛﺘﺐ‬ ‫؟‬ ‫ﺗﻔﺎﺡ‬ ‫ﺷﺠﺮﺓ‬ ‫ﻇﻞ‬ ‫ﻓﻲ‬ ‫ﺟﻠﺲ‬ ‫ﻗﺪ‬ ‫ﻳﻜﻮﻥ‬ ‫ﺃﻥ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻓﻤﺎ‬
.‫ﻣﺘﻤﻤﺘﻬﺎ؟‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻓﻤﺎ‬ ،% ٣٧ ‫ﻫﻮ‬ ‫ﹴ‬‫ﻏﺪ‬ ‫ﻳﻮﻡ‬ ‫ﺍﻷﻣﻄﺎﺭ‬ ‫ﺗﺴﺎﻗﻂ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻛﺎﻥ‬ ‫ﺇﺫﺍ‬  
‫ﺍﻟﻜﺘﺐ‬ ‫ﺃﺣﺪ‬ ‫ﺍﺧﺘﺮﻧﺎ‬ ‫ﺇﺫﺍ‬ .‫ﺎ‬‫ﹼﹰ‬‫ﻴ‬‫ﻋﻠﻤ‬ ‫ﹰ‬‫ﺎ‬‫ﻛﺘﺎﺑ‬ ٥٢ ‫ﺑﻴﻨﻬﺎ‬ ‫ﻣﻦ‬ ، ‫ﹰ‬‫ﺎ‬‫ﻛﺘﺎﺑ‬ ٩٠ ‫ﺻﻔﻴﺔ‬ ‫ﻣﻜﺘﺒﺔ‬ ‫ﻓﻲ‬  
‫؟‬ ‫ﺎ‬‫ﹼﹰ‬‫ﻴ‬‫ﻋﻠﻤ‬ ‫ﺍﻟﻜﺘﺎﺏ‬ ‫ﻳﻜﻮﻥ‬ ‫ﺃﻻ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻓﻤﺎ‬ ،‫ﺎ‬‫ﹼﹰ‬‫ﻴ‬‫ﻋﺸﻮﺍﺋ‬
‫ﻛﻞ‬ ‫ﻣﻦ‬ ‫ﻛﺮﺓ‬ ‫ﻛﻢ‬ .‫ﺧﻀﺮﺍﺀ‬ ٨‫ﻭ‬ ،‫ﺯﺭﻗﺎﺀ‬ ٤ ‫ﻭ‬ ،‫ﺣﻤﺮﺍﺀ‬ ‫ﻛﺮﺍﺕ‬ ٦ ‫ﻛﻴﺲ‬ ‫ﻳﺤﻮﻱ‬  
‫؟‬ ‫ﻟﻮﻥ‬ ‫ﻛﻞ‬ ‫ﻣﻦ‬ ‫ﻛﺮﺓ‬ ‫ﺍﺧﺘﻴﺎﺭ‬ ‫ﺍﺣﺘﻤﺎﻝ‬ ‫ﻳﺘﻐﻴﺮ‬ ‫ﻻ‬ ‫ﺑﺤﻴﺚ‬ ‫ﺍﻟﻜﻴﺲ‬ ‫ﺇﻟﻰ‬ ‫ﺇﺿﺎﻓﺘﻬﺎ‬ ‫ﻳﻤﻜﻦ‬ ‫ﻟﻮﻥ‬
.‫ﺇﺟﺎﺑﺘﻚ‬ ‫ﻞ‬‫ﹼ‬‫ﻠ‬‫ﻋ‬
.‫ﺇﺟﺎﺑﺘﻚ‬ ‫ﻞ‬‫ﹼ‬‫ﻠ‬‫ﻭﻋ‬ .‫ﻭﻣﺘﻤﻤﺘﻬﺎ‬ ‫ﺣﺎﺩﺛﺔ‬ ‫ﺍﺣﺘﻤﺎﻻﺕ‬ ‫ﻞ‬‫ﹼ‬‫ﺜ‬‫ﻳﻤ‬ ‫ﻻ‬ ‫ﺍﻟﺬﻱ‬ ‫ﺍﻻﺣﺘﻤﺎﻻﺕ‬ ‫ﺯﻭﺝ‬ ‫ﻦ‬‫ﹼ‬‫ﻴ‬‫ﻋ‬ 
(٠٫٤٤ ، ٠٫٣٣) (١
٤ ، ٦
٨ ) (٣
٨ ، ٠٫٦٢٥) (٢
٥ ، ٣
٥ )
‫ﺇﺫﺍ‬ .‫ﺃﺑﻴﺾ‬ ‫ﻭﺟﻮﺭﺏ‬ ،‫ﺑﻨﻴﺎﻥ‬ ‫ﻭﺟﻮﺭﺑﺎﻥ‬ ، ‫ﺳﻮﺩﺍﺀ‬ ‫ﺟﻮﺍﺭﺏ‬ ٥ ‫ﺳﻌﻴﺪ‬ ‫ﻋﻨﺪ‬   
.‫ﻻ‬ ‫ﺃﻡ‬ ‫ﻣﻌﻘﻮﻟﺔ‬ ‫ﺍﻟﺘﺎﻟﻴﺔ‬ ‫ﺍﻻﺣﺘﻤﺎﻻﺕ‬ ‫ﻛﺎﻧﺖ‬ ‫ﺇﺫﺍ‬ ‫ﻣﺎ‬ ‫ﻓﺤﺪﺩ‬ ،‫ﻋﺸﻮﺍﺋﻴﺔ‬ ‫ﺑﻄﺮﻳﻘﺔ‬ ‫ﹰ‬‫ﺎ‬‫ﺟﻮﺭﺑ‬ ‫ﺍﺧﺘﺎﺭ‬
.‫ﺇﺟﺎﺑﺘﻚ‬ ‫ﻞ‬‫ﹼ‬‫ﻠ‬‫ﻭﻋ‬
١
٤ = ( ‫ﺑﻨﻲ‬ )‫ﺡ‬ (‫ﺝ‬ ٤
٥ = ( ‫ﺃﺑﻴﺾ‬ )‫ﺡ‬ (‫ﺏ‬ ١
٣ = ( ‫ﺃﺳﻮﺩ‬ )‫ﺡ‬ (‫ﺃ‬
‫ﺍﻟﻤﺸﺎﺭﻛﻮﻥ‬
‫ﺫﻛﻮﺭ‬٢٥
‫ﺇﻧﺎﺙ‬١٥
‫ﺍﻟﻄﺎﺋﻒ‬ ‫ﻣﺪﻳﻨﺔ‬١٠
‫ﻣﻜﺔ‬ ‫ﻣﺪﻳﻨﺔ‬١٦
‫ﺟﺪﺓ‬ ‫ﻣﺪﻳﻨﺔ‬١٤
 

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