Respuesta :
As per given by the question,
There are given that, 4 green marbles and 1 blue marble contains in a box and pick a marble at randomly.
Now,
Here pick a marble out at random, so first pick a marble for blue;
Then,
Total number of green marbles is 4, and the total number of blue marble is 1, and;
The total numbers of marbles in a bag is, 4+1=5.
So,
For pick the blue marble from 5 marble,
Now,
[tex]\begin{gathered} 5_{C_1}=\frac{5!}{1!\times(5-1)!} \\ =\frac{5!}{1!\times4!} \\ =\frac{5\times4!}{1!\times4!} \\ =5 \end{gathered}[/tex]Now, for pick the green marble from 5 marbles.
Here, total green marble is 4.
So,
[tex]\begin{gathered} 5_{C_4}=\frac{5!}{4!\times(5-4)!} \\ =\frac{5\times4!}{4!\times1!} \\ =5 \end{gathered}[/tex]Now,
From the question, there are clearly mention that if pick a blue, then stop because you won 20 points.
So,
Probability of the blue marble that won the 20 points.
then,
[tex]\begin{gathered} P(x=20)=\frac{total\text{ number of blue marble}}{\text{total number of marble}} \\ P(x=20)=\frac{1}{5} \end{gathered}[/tex]Now,
There are also mention that, pick a green marbles without replacing and if its blue then win the 10 points,
So,
probability of the blue marbles that won 10 pointss is,
[tex]P(x=10)=\frac{1}{4}[/tex]Now,
Here, find the probability that no points for the first green ball is,
[tex]P(x=0)=\frac{4}{5}[/tex]Now,
If you played this game 100 time, then the probability is,
[tex]\begin{gathered} P(x=0)+_{}P(x=10)+P(x=20)=\frac{4}{5}+\frac{1}{4}+\frac{1}{5} \\ =1.25 \end{gathered}[/tex]now,
For 100 times,
[tex]1.25\times100=125\text{ points.}[/tex]Hence, 125 points can you expect to win.
