Answer: The correct option is (D) 0.9701.
Step-by-step explanation: Given that a bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles. Three marbles are randomly chosen from the bag.
We are to find the probability that there is at most one purple marble if three marbles are chosen at random.
Here,
number of yellow marbles = 8,
number of green marbles = 9,
number of purple marbles = 3
and
number of red marbles = 5.
So, total number of marbles = 8 + 9 + 3 + 5 = 25.
If there is at most one purple marble, then there can be 0 or 1 purple marble in the three randomly chosen marbles.
Therefore, the probability that that there is at most one purple marble if three marbles are chosen at random is given by
[tex]P\\\\\\=P(X=0)+P(X=1)\\\\\\=\dfrac{^{22}C_3}{^{25}C_3}+\dfrac{^3C_1\times ^{22}C_2}{^{25}C_3}\\\\\\=\dfrac{\frac{22!}{3!(22-3)!}}{\frac{25!}{3!(25-3)!}}+\dfrac{3\times \frac{22!}{2!(22-2)!}}{\frac{25!}{3!(25-3)!}}\\\\\\=\dfrac{22!}{3!19!}\times\dfrac{3!22!}{25!}+\dfrac{3\times22!}{2!20!}\times\dfrac{3!22!}{25!}\\\\\\=\dfrac{22\times21\times20}{25\times24\times23}+9\times \dfrac{22\times21}{25\times24\times23}\\\\\\=0.6695+9\times 0.0334\\\\\\=0.9701.[/tex]
Thus, the required probability is 0.9701.
Option (D) is correct.
The probability that there is at most one purple marble is 0.9701.
Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen. It is the ratio of the favorable event to the total number of events.
Given
A bag contains eight yellow marbles, nine green marbles, three purple marbles, and five red marbles.
To find
The probability that there is at most one purple marble.
So the total balls = 8 + 9 + 3 + 5 = 25
Three marble chosen randomly.
[tex]\rm = P(x=0) + P(x=1)\\\\= \dfrac{^{22}C__3 }{^{25}C__3 } + \dfrac{^{3}C_{1} * ^{22}C_2 }{^{25}C_3 }[/tex]
[tex]= 0.6695 + 3 * 0.0336\\\\= 0.9701[/tex]
So the probability is 0.9701.
More about the probability link is given below.
https://brainly.com/question/743546
