There are some coloured pins in a bag

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

∵ 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

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step-by-step explanation:

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