11. 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 Else we roll a die with distribution - 1, 2, 3, 4 1 2 3 4 0.2 0.3 0.2 0.3 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 independent?
11. 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 Else we roll a die with distribution - 1, 2, 3, 4 1 2 3 4 0.2 0.3 0.2 0.3 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 independent?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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Transcribed Image Text:11. 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
Else we roll a die with distribution
-
1, 2, 3, 4
1
2
3
4
0.2
0.3 0.2 0.3
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 independent?
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