Respuesta :
Answer:
(a) [tex]\frac{r}{100}[/tex]
(b) [tex]\frac{r}{100}[/tex]
(c) [tex]\frac{r}{100}[/tex]
Step-by-step explanation:
Given,
The total number of balls = 100,
Red balls = r
So, the remaining balls = 100 - r,
(a) ∵ The probability that first ball drawn will be red
[tex]=\frac{\text{Red balls}}{\text{Total balls}}[/tex]
[tex]=\frac{r}{100}[/tex]
(b) Also, the probability of a ball other than red ball = [tex]1-\frac{r}{100}[/tex]
[tex]=\frac{100-r}{100}[/tex]
So, the probability of getting red ball in second thrawn( one is red second is red or one is not red second is red ),
[tex]=\frac{r}{100}\times \frac{r-1}{99}+\frac{100-r}{100}\times \frac{r}{99}[/tex]
[tex]=\frac{r}{99}[\frac{r-1}{100}+\frac{100-r}{100}][/tex]
[tex]=\frac{r}{99}[\frac{r-1+100-r}{100}][/tex]
[tex]=\frac{r}{99}[\frac{99}{100}][/tex]
[tex]=\frac{r}{100}[/tex]
Now, the the probability of getting red ball in third thrawn,
[tex]=\frac{r}{100}\times \frac{r-1}{99}\times \frac{r-2}{98}+\frac{100-r}{100}\times \frac{r}{99}\times \frac{r-1}{98}+\frac{100-r}{100}\times \frac{99-r}{99}\times \frac{r}{98}[/tex]
[tex]=\frac{r}{100}[/tex]
......so on,...
This pattern will be followed in every trials,
Hence, the probability that the 50th ball drawn will be red = [tex]\frac{r}{100}[/tex]
(c) Similarly, Â the probability that the last ball drawn will be red = [tex]\frac{r}{100}[/tex]
