Ex 7.4, 2

Transcript

Ex 7.4, 2 (i) 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. (i) What are the possible outcomes of the pen colours? Can you draw a tree diagram representing the possible outcomes? Let’s draw our tree diagram Note: Because there are 3 red pens, 4 black pens and 2 green pens Probability of getting red = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑟𝑒𝑑 𝑝𝑒𝑛𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑝𝑒𝑛𝑠) = 3/(3 + 4 + 2)=𝟑/𝟗 And, Probability of getting black = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑙𝑎𝑐𝑘 𝑝𝑒𝑛𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑝𝑒𝑛𝑠) = 𝟒/𝟗 Probability of getting green = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑔𝑟𝑒𝑒𝑛 𝑝𝑒𝑛𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑝𝑒𝑛𝑠) = 𝟐/𝟗 Ex 7.4, 2 (ii) 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. (ii) Can you use the tree diagram to guess the probability that both you and your friend pick pens of the same colour? We need to find probability we get Red, Red Black, Black Green, Green Using our tree diagram Now, P(red, red) = 𝟑/𝟗 ×𝟑/𝟗=𝟗/𝟖𝟏 P(black, black) = 𝟒/𝟗 ×𝟒/𝟗=16/81 P(green, green) = 𝟐/𝟗 ×𝟐/𝟗=𝟒/𝟖𝟏 Thus, Probability of getting same color = P(red, red) + P(black, black) + P(green, green) = 9/81+16/81+4/81 = 𝟐𝟗/𝟖𝟏