Respuesta :
Step-by-step explanation:
Consider the provided information.
Bag contains 8 red marbles, 6 white marbles, and 8 blue marbles.
Total number of marbles = 8+6+8=22
The probability of getting a red marbles: 8/22
The probability of not getting a red marbles: 14/22
Now consider the part A:
We need to find probability that all the marbles are red if 4 marbles drawn.
The probability that all marbles are red is:
[tex]\frac{8}{22}\cdot\frac{7}{21}\cdot\frac{6}{20}\cdot\frac{5}{19}=0.009569[/tex]
Hence, the probability that all marbles are red is 0.009569
Part B
Find the probability that exactly two of the marbles are red.
The probability that exactly 2 marbles are red is:
[tex]\frac{8}{22}\cdot\frac{7}{21}\cdot\frac{14}{20}\cdot\frac{13}{19}=0.0581[/tex]
Hence, the probability that exactly two red marbles is 0.0581
Part C
Now find the probability that none of the marbles are red.
The probability that none of the marbles are red is:
[tex]\frac{14}{22}\cdot\frac{13}{21}\cdot\frac{12}{20}\cdot\frac{11}{19}=0.1368[/tex]
Hence, the probability that none of the marbles are red is 0.1368
The probability that all the marbles are red is 0.009569, the probability that exactly two of the marbles are red is 0.0581, and the probability that none of the marbles are red is 0.1368.
Given :
- A bag contains 8 red marbles, 6 white marbles, and 8 blue marbles.
- You draw 4 marbles out at random, without replacement.
According to the given data, 8/22 is the probability of getting the red marble and 14/22 is the probability of not getting the red marble.
A) The probability that all the marbles are red is given by:
[tex]=\dfrac{8}{22}\times \dfrac{7}{21}\times \dfrac{6}{20} \times \dfrac{5}{19}[/tex]
[tex]= 0.009569[/tex]
B) The probability that exactly two of the marbles are red is given by:
[tex]=\dfrac{8}{22}\times \dfrac{7}{21}\times \dfrac{14}{20} \times \dfrac{13}{19}[/tex]
= 0.0581
C) The probability that none of the marbles are red is given by:
[tex]=\dfrac{14}{22}\times \dfrac{13}{21}\times \dfrac{12}{20} \times \dfrac{11}{19}[/tex]
= 0.1368
For more information, refer to the link given below:
https://brainly.com/question/23017717
