2. Consider the following three step experiment: Step1: Choose a coin from a bag containing 10 coins, 5 of which are fair F, and the remaining unfair U with P(H) = 0.8. Step2: toss the chosen coin (can land H or T) in Step (1). Step 3: If the coin lands H we roll a fair 4-sided die with labels 3, 4 Else we roll a die with distribution - 1, 2, 1 2 3 4 0.2 0.3 0.2 0.3 1 Let E = Die rolls to an even number, and F = tossed coin is a fair coin, G Coin lands heads. (a) Draw a labelled tree diagram for this experiment. (b) List out all outcomes in the events E, F, and G. (c) Calculate P(E), P(F), P(G), P(E|F), P(F|G), P(E|G) (d) Are E and F independent? Are F and G independent? Are E and G indepen- dent?
2. Consider the following three step experiment: Step1: Choose a coin from a bag containing 10 coins, 5 of which are fair F, and the remaining unfair U with P(H) = 0.8. Step2: toss the chosen coin (can land H or T) in Step (1). Step 3: If the coin lands H we roll a fair 4-sided die with labels 3, 4 Else we roll a die with distribution - 1, 2, 1 2 3 4 0.2 0.3 0.2 0.3 1 Let E = Die rolls to an even number, and F = tossed coin is a fair coin, G Coin lands heads. (a) Draw a labelled tree diagram for this experiment. (b) List out all outcomes in the events E, F, and G. (c) Calculate P(E), P(F), P(G), P(E|F), P(F|G), P(E|G) (d) Are E and F independent? Are F and G independent? Are E and G indepen- dent?
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 10CYU
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Transcribed Image Text:2. Consider the following three step experiment:
Step1: Choose a coin from a bag containing 10 coins, 5 of which are fair F,
and the remaining unfair U with P(H) = 0.8.
Step2: toss the chosen coin (can land H or T) in Step (1).
Step 3: If the coin lands H we roll a fair 4-sided die with labels
3, 4
Else we roll a die with distribution
-
1, 2,
1 2 3 4
0.2 0.3 0.2 0.3
1
Let E
=
Die rolls to an even number, and F = tossed coin is a fair coin, G
Coin lands heads.
(a) Draw a labelled tree diagram for this experiment.
(b) List out all outcomes in the events E, F, and G.
(c) Calculate P(E), P(F), P(G), P(E|F), P(F|G), P(E|G)
(d) Are E and F independent? Are F and G independent? Are E and G indepen-
dent?
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