Final answer:
To complete the table and find the number of green pins in the bag, we need to use the given probabilities and information. Solve the equation to find the probability of picking a yellow pin and then calculate the probability of picking a green pin. Then, use the number of purple pins to find the number of green pins in the bag.
Step-by-step explanation:
To solve this problem, we need to use the given information and some basic probability concepts. Let's break it down step-by-step:
a) Since the table only shows the probabilities of picking a purple or gray pin, we need to find the probabilities of picking a green or yellow pin. We know that the probability of picking a green pin is three times the probability of picking a yellow pin. Let the probability of picking a yellow pin be 'y'. So, the probability of picking a green pin is 3y. Since the total probability is 1, we can write an equation: 3y + y + 0.35 + 0.25 = 1. Simplifying this equation will give us the value of 'y' and then we can find the probability of picking a green pin.
b) We are given that there are 14 purple pins in the bag. Therefore, the total number of pins in the bag is the sum of the number of purple pins, green pins, yellow pins, and gray pins. Using this information, we can calculate the number of green pins in the bag.