1. COMPOUND EVENTS Grade 7 – Chadwick International School

2. Learning objectives Solve compound event problems (independent & dependent events)

3. Independent Event Dependent Event with replacementwithout replacement

4. Tom picks a marble at random. He returns the marble to the pile and then picks another marble at random. Is this an independent or dependent event? An independent event.

5. 17) Jake picks a card. He keeps the card and then picks another one. Is this an independent or dependent event? 214 3 Dependent event

6. 16) Stephanie spins the spinner twice. Is this an independent or dependent event? An independent event

7. Carson picks a marble at random. He does not put the first marble back. Again he picks another marble. What is P(purple, purple)? Simplify. P(purple) = P(purple, purple) P(purple) x x 3 7 P(purple, purple) = Want Total

8. Want Total Carson picks a marble at random. He does not put the first marble back. Again he picks another marble. What is P(purple, purple)? Simplify. P(purple) = P(purple, purple) P(purple) x x 3 7 P(purple, purple) = 2 6 = 6 42

9. Carson picks a marble at random. He does not put the first marble back. Again he picks another marble. What is P(purple, purple)? Simplify. P(purple) = P(purple, purple) P(purple) x x 3 7 P(purple, purple) = 2 6 = 1 7

10. Ty pick a card. He keeps the first card and then picks another card. What is P(less than 8, less than 8)? Simplify. Want Total P(<8) = P(<8,<8) P(<8) x x 3 4 P(<8,<8) = 658677685 6 5 7 8 5 6 7 57

11. Ty pick a card. He keeps the first card and then picks another card. What is P(less than 8, less than 8)? Simplify. P(<8) = x x 3 4 = 65867768 6 5 7 8 5 6 7 Want Total 2 3 = 6 12 6 5 7 8 6 7 = 1 2 7 P(<8,<8)

12. Solve. Using the spinner below, what is the probability of spinning a 2 on your first spin, and either a 3 or a 1 on your second spin? You put the letters SCHOOL into a bag. What is the probability that you pull a L out on your first pick, set it aside, and then pull a vowel? You have 6 cards numbered 1-6 in a pile. What is the probability that on your first pick you get an odd numbered card (keeping the card), and then on your second pick you get a number less than 7?

13. Pick 1Pick 2 R G R G R G 2/10 8/10 1/9 8/9 2/9 7/9 P(R,R)=2/10x 1/9= P(R,G)=2/10x 8/9 = P(G,R)= 8/10 x 1/9= P(G)= 8/10 x 7/0 = 2/90 16/90 8/90 56/90* I have a bag with 2 red and 8 green counters. I pick out a counter, don’t put it back, and pick another. Draw a tree diagram for this situation.

14. What is the probability that I pick one of each? If this happens I pick red then green OR green then red. When I see OR I know I have to add the probabilities So... P(RG) + P(GR) 16/90+16/90= 32/90 Pick 1Pick 2 R G R G R G 2/10 8/10 1/9 8/9 2/9 7/9 P(RR)=2/10x 1/9= P(RG)=2/10x 8/9 = P(GR)= 8/10 x 2/9= P(G)= 8/10 x 7/9 = 2/90 16/90 56/90

15. Pick 1Pick 2 W D W D W D 7/12 5/12 6/11 5/11 7/11 4/11 P(WW)=7/12 X 6/11= P(WD)=7/12 X 5/11= P(DW)=5/12 X 7/11= P(DD)=5/12 X 4/11= 42/132 35/132 20/132 I have a bag of chocolates 12, they are white chocolate or dark chocolate. 7 of the chocolates are white chocolates. I pick one at random, eat it and pick another Draw a tree diagram for this situation.

16. What is the probability that I have one of each? If this happens I will have a white then dark OR a dark then white. When I see OR I know I have to add the probabilities So... P(WD) + P(DW) = 35/132 + 35/132= 70/132 or 35/66 Pick 1Pick 2 W D W D W D 7/12 5/12 6/11 5/11 7/11 4/11 P(WW)=7/12 X 6/11= P(WD)=7/12 X 5/11= P(DW)=5/12 X 7/11= P(DD)=5/12 X 4/11= 42/132 35/132 20/132

18. 1.I have a bag of sweets, the sweets are toffees and fruit drops. There are 8 toffees and 6 fruit drops. I have a sweet at random then I my mate has one at random. Find the probability that: a)I have a toffee and my friend has a fruit drop b)We both have fruit drops c)We both have the same d)We end up with different sweets 2. There are 10 pupils in my class, 4 boys and 6 girls. I need three of them to do a job for me. I select one pupil at a time at random, no pupil will be selected twice. What is the probability that the people doing the jobs will be: a)3 boys b)3 girls c)1 boy and 2 girls What is the probability that: a)The second job will be done by a giirl? b) There will be at least 1 boy. 3. Alan is going to sit two exams, his performance is affected by his confidence. The probability he will pass the first exam is 0.7. If he passes the first exam the probability he passes the second is 0.9. If he fails the first exam the probability he will pass the second is 0.3. What is the probability that: a)He will pass both exams b)He won’t pass either exam c)He will only pass one exam 4. If have 20 counters in a bag, ten red, 6 blue and 4 yellow. I pick out a counter, don’t replace it, then I pick out another. What is the probability that I have: a)2 reds b)No reds c)A yellow then a blue d)A yellow and a blue e)The second counter as red f)Both counters the same colour Answers: 1) a)48/182 b) 30/182 c)86/182 d)96/182 1) a) 24/720 b)120/720 c) 360/720 d) 240/720 e)600/720 Answers: 4) a)0.63 b)0.21 c)0.16 5) a)90/380 b)24/380 c)90/380 d)48/390 e)190/380 f) 132/390