Question

Topic 5: Tree Diagrams Tree Diagrams A tree diagram is great for solving probability problems that multiple stages. The probabilities of corresponding branches. Then multipl the probability of that particular sequence of events occurring involve successive events or each outcome for each stage are written on the ying the probabilities along a sequence of branches yields 1. Betsy flips a coin three times. The sample space of possible outcomes diagram below. Label the branches with the appropriate probabilities. is shown in the tree 1st toss 2nd toss 3rdtoss Outcomes HH,H) T (MHT) OS(H,T,H) THTD T,H,H) Head Find: 0.5H a) P(she gets head on every flip) Tail 5 (LLH) (T,T,T) ,18= 0.12 s b) P(she gets the same thing on every flip) 213 = o.25 c) P(exactly one flip is heads) d) P(at least one flip is heads) 75-о.$15 e) Complete the table below: 2 # heads requency robability 0 0.12S .275 0.375 0.125

Please answer all of the questions completely and show your work. Disregard the work already written. Thank you!

Answer 1

Tree Diagram

0.5 H 0.5 0.5 T HHT Head 0.5H 0.5 0.5 0.5 T HTT H THH 0.5 T THT 0.5 0.5 Tail 0.5 H TTH 0.5 0

a) P(head on very flip) = 0.5x0.5x0.5 = 0.125

b) P(she get the same on every flip) = P(HHH) + P(TTT)

= 0.125 x 2

= 0.250

c) P(exactly one flip is heads) = 3/8

= 0.375

d) P(at least one flip is heads) = 1 - P(all tails)

= 1 - 0.125

= 0.875

e)

X = #heads	0	1	2	3
Frequency	1	3	3	1
Probability	1/8 = 0.125	3/8 = 0.375	3/8 = 0.375	1/8 = 0.125