Following are the calculation on the given probability:
Given:
Please find the given question.
To find:
probability=?
Solution:
We assume that the probability of throwing a sum of 10 in a pair of fair dice is:
[tex]=\frac{\bold{n((5,5),(6,4),(4,6))}}{\bold{n (all events)}} \\\\ \bold{=\frac{3}{36} = 0.0833}[/tex]
Now assume that the chance of discovering the number of occurrences can be represented by a Binomial distribution with p= 0.0833 and n= 10.
[tex]\to\bold{P(X=r)= ^nC_r \times p^r \times (1-p)^{n-r}}[/tex]
Thus,
[tex]\bold{P(X>=9)= P(X=9)+P(X=10)}[/tex]
[tex]\bold{= ^{10}C_{9} \times 0.0833^{9} \times (0.9167)^1 + ^{10}C_{10}\times 0.0833^{10} \times (0.9167)^0}\\\\\bold{= \frac{10!}{9!(10-9)!} \times 1.931 \times 0.9167+ \frac{10!}{10!(10-10)!}\times1.608 \times 1}\\\\\bold{= \frac{10 \times 9!}{9! \ 1!} \times 1.770+ \frac{10!}{10!\ 0!}\times1.608}\\\\\bold{= 10 \times 1.770+ 1\times1.608}\\\\\bold{= 17.70+ 1.608}\\\\\bold{= 19.308}\\\\[/tex]
Therefore, the final answer is "19.308".
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