Three horses in a race. The probability that the first horse is twice as likely to win as the second horse and the second horse is 3 times as likely to win as the third horse. Find the probability that the first horse or the second horse win.

  • احصاء
  • رياضيات

Three horses in a race. The probability that the first horse is twice as likely to win as the second horse and the second horse is 3 times as likely to win as the third horse. Find the probability that the first horse or the second horse win.

الأجوبة

h_1={first horse wins}
h_2={second horse wins}
h_3={third horse wins}
Un balanced weight, mutual exclusive events →h_1∩h_2∩h_3=∅
∑probilities=1  →  P(h_1 )+P(h_2 )+P(h_3 )=1
P(h_1 )=2P(h_2 )     ,    P(h_2 )=3P(h_3 )   ,P(h_1 )=6P(h_3 )
P(h_3 )هو اصغر احتمال فهفرض ان قيمته w
P(h_3 )=w  ,P(h_2 )=3w  ,P(h_1 )=6w  
6w+3w+w=1   →10w=1→w=1/10
P(h_3 )=1/10   ,P(h_2 )=3/10   ,P(h_1 )=6/10   
The probability that the first horse or the second horse win is:
P(h_1∪h_2 )=P(h_1 )+P(h_2 )-P(h_1∩h_2 )=6/10+3/10  -0=9/10 

هل كان المحتوى مفيد؟

تبحث عن مدرس اونلاين؟

محتاج مساعدة باختيار المدرس الافضل؟ تواصل مع فريقنا الان لمساعدتك بتأمين افضل مدرس
ماهو التخصص الذي تبحث عنه؟
اكتب هنا...