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
- 2021-05-04
- HebaAallahFathy
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
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