Question

Probablity question

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{India plays two matches each with New Zealand and South Africa.} \hspace{.33em}\\~\\
& \normalsize \text{ In any match , the probability of different outcomes for India} \hspace{.33em}\\~\\
& \normalsize \text{ is given below -} \hspace{.33em}\\~\\~\\~\\
& \begin{array}{|c|c|c|} \hline
\text{Outcome} & \text{Win} & \text{Loss} & \text{Draw} \\ \hline
\text{Probablity} & 0.5 & 0.45 & 0.05 \\ \hline
\text{Points} & 2 & 0 & 1 \\ \hline
\end{array}
& \hspace{.33em}\\~\\
& \normalsize \text{1.) What is the probablity india getting atleast 7 points .} \hspace{.33em}\\~\\
& \normalsize \text{in the contest ? assume south africa and newzealand } \hspace{.33em}\\~\\
& \normalsize \text{play 2 matches. } \hspace{.33em}\\~\\
& \normalsize \text{2.) What is the probablity Soth africa getting atleast 4 points .} \hspace{.33em}\\~\\
& \normalsize \text{ assume south africa and newzealand play 2 matches. } \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

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)

Answer 3

how come this
prob(8pts) = (.5)^4

Answer 4

there is .5 chance of winning each match, each match is independent event, so multiply probabilites

.5*.5*.5*.5 = (.5)^4

Answer 5

ok then here where \(\color{red}{4}\) comes from

prob(7pts) = \(\color{red}{4}\)*(.5)^3 *.05

Answer 6

ok there are 4 ways to have

2221
1222
2122
2212

is it this ?

Answer 7

correct

Answer 8

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

Answer 9

actually it may be easier to find p(0), p(1), p(2), p(3)
then subtract there total from 1

\[P(x \ge 4) = 1 - P(x<4)\]

Answer 10

thanks