mathmath333
  • mathmath333
Probablity question
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{India plays two matches each with New Zealand and South Africa.} \hspace{.33em}\\~\\ & \normalsize \text{ In any match , the probability of different outcomes for India} \hspace{.33em}\\~\\ & \normalsize \text{ is given below -} \hspace{.33em}\\~\\~\\~\\ & \begin{array}{|c|c|c|} \hline \text{Outcome} & \text{Win} & \text{Loss} & \text{Draw} \\ \hline \text{Probablity} & 0.5 & 0.45 & 0.05 \\ \hline \text{Points} & 2 & 0 & 1 \\ \hline \end{array} & \hspace{.33em}\\~\\ & \normalsize \text{1.) What is the probablity india getting atleast 7 points .} \hspace{.33em}\\~\\ & \normalsize \text{in the contest ? assume south africa and newzealand } \hspace{.33em}\\~\\ & \normalsize \text{play 2 matches. } \hspace{.33em}\\~\\ & \normalsize \text{2.) What is the probablity Soth africa getting atleast 4 points .} \hspace{.33em}\\~\\ & \normalsize \text{ assume south africa and newzealand play 2 matches. } \hspace{.33em}\\~\\ \end{align}}\)
dumbcow
  • dumbcow
you have to do it case by case prob(8pts) = (.5)^4 because they have to win all 4 games prob(7pts) = 4*(.5)^3 *.05 because you have to win 3 and tie 1 (there are 4 ways this could happen) to find "at least 7 pts", you must add up prob(7) + prob(8)
mathmath333
  • mathmath333
how come this prob(8pts) = (.5)^4

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dumbcow
  • dumbcow
there is .5 chance of winning each match, each match is independent event, so multiply probabilites .5*.5*.5*.5 = (.5)^4
mathmath333
  • mathmath333
ok then here where \(\color{red}{4}\) comes from prob(7pts) = \(\color{red}{4}\)*(.5)^3 *.05
mathmath333
  • mathmath333
ok there are 4 ways to have 2221 1222 2122 2212 is it this ?
dumbcow
  • dumbcow
correct
dumbcow
  • dumbcow
for part 2, there are more cases you need to find p(4), p(5), p(6), p(7), p(8) and add them all up
dumbcow
  • dumbcow
actually it may be easier to find p(0), p(1), p(2), p(3) then subtract there total from 1 \[P(x \ge 4) = 1 - P(x<4)\]
mathmath333
  • mathmath333
thanks

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