Let us say that you have a box containing 3 red pens, 4 black pens and 2 green pens. Class 9

Let us say that you have a box containing 3 red pens, 4 black pens and 2 green pens. Class 9

Question 1.

Let us say that you have a box containing 3 red pens, 4 black pens and 2 green pens. You pick a pen (without looking) from the box and put it back. Then your friend does the same. Class 9

i. What are the possible outcomes of the pen colours? Can you draw a tree diagram representing the possible outcomes?

ii. Can you use the tree diagram to guess the probability that both you and your friend pick pens of the same colour?

Solution:

i. Since the pen is put back, the total number of pens remains the same for both picks.

Let R = Red, B = Black, G = Green

∴ Possible outcomes = Sample space

S = {(Red, Red), (Red, Black), (Red, Green), (Black, Red), (Black, Black), (Black, Green), (Green, Red), (Green, Black), (Green, Green)}

ii. Same colour meAnswer: {RR, BB, GG}

P(pens of the same colour)

$=\frac{\text { Number of possible outcomes }}{\text { Total number of outcomes }}=\frac{3}{9}=\frac{1}{3}=0.33$

∴ The probability that both pick pen of same colour is 0.33