Respuesta :
The probability that after re-rolling these three dice, at least three of the five dice show the same value is [tex]\frac{4}{9}[/tex]
Of the three dice rolled, one may match the original pair and two are different, and this can occur three ways:
[tex](\frac16 \times \frac56 \times \frac56 ) + ( \frac56 \times \frac16 \times \frac56 ) + ( \frac56 \times \frac 56 \times \frac 16 ) = \frac {75}{216}[/tex]
[ where [tex]\frac{1}{6}[/tex] is the probability of matching the first two and [tex]\frac{5}{6}[/tex] is the probability of not matching the first two ]
Or, two may match the original pair and one is different
[tex]( \frac16 \times \frac16 \times \frac 56 ) + ( \frac16 \times \frac56 \times \frac 16 ) + ( \frac56 \times \frac16 \times \frac16 ) = \frac {15}{216}[/tex]
Or, all three may match the original pair
[tex]( \frac 16 \times \frac 16 \times \frac 16 ) = \frac {1}{216}[/tex]
Or, all three may be the same, but not match the original pair:
[tex]( \frac 56 \times \frac 16 \times\frac 16 ) = \frac {5}{216}[/tex]
[ where [tex]\frac{5}{6}[/tex] is the probability of getting a new number and [tex]\frac{1}{6}[/tex] is the probability of matching that new number ]
Adding these together: [tex]\frac {75}{216} + \frac {15}{216} + \frac 1{216} + \frac 5{216} = \frac {96}{216} = \frac 49[/tex]
To learn more about probability with the given link
https://brainly.com/question/11234923
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