Answer:
Green is 0.3, Yellow is 0.1
There are 12 green pins in the bag
Step-by-step explanation:
The probability is the ratio between the possible outcomes over the total outcomes
- The value of the probability of possible outcomes is greater than 0 and smaller than 1 (0 < P < 1)
- The sum of the probabilities of all outcomes must equal 1
∵ A bag contains some green, yellow, purple and grey pins
∵ The probability of picking a purple pin P(purple) = 0.35
∵ The probability of picking a grey pin P(grey) = 0.25
→ The total of all possible outcomes is 1
∴ The sum of the probability of green and yellow pins = 1 - 0.35 - 0.25
∴ The sum of the probability of green and yellow pins = 0.4
∴ P(green) + P(yellow) = 0.4 ⇒ (1)
∵ The probability of picking a green pin is 3 times the probability
of picking a yellow pin
∴ P(green) = 3 P(yellow) ⇒ (2)
→ Substitute (2) in (1)
∴ 3 P(yellow) + P(yellow) = 0.4
∴ 4 P(yellow) = 0.4
→ Divide both sides by 4
∴ P(yellow) = 0.1
∴ The probability of picking a yellow pin is 0.1
→ Substitute P(yellow) in (20 by 0.1
∴ P(green) = 3(0.1)
∴ P(green) = 0.3
∴ The probability of picking a green pin is 0.3
∴ Green = 0.3, Yellow = 0.1
∵ There are 14 purple pins in the bag
∵ P(purple) = 0.35
∴ 0.35 of purple pins = 14
→ To find the total number of pins in the bag divide 14 by 0.35
∴ The total number of pins = 14 ÷ 0.35
∴ The total number of pins = 40 pins
∵ P(green) = 0.3
∴ The number of green pins = 0.3 × 40
∴ The number of green pins = 12 pins
∴ There are 12 green pins in the bag
