Now use the histogram or table to answer the following questions. 1. What is the probability of flipping 3 coins and all three landing on heads? P( H ) = | (Enter your answer as a decimal. Do not round.) HINT: Change the fraction to a decimal. 2. What is the probability of flipping 3 coins and getting 1 or 3 heads? P( H) + + P( T) (Enter the outcomes in numerical order. Enter your final answer only. Use the decimal form of the probability. Do not round.) 3. What is the probability of flipping 3 coins and not getting 2 heads? P(x + 2) = 6 (Enter the final answer only. Use decimal form of the probability. Do not round.)

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Let's say we are interested in the probability number of heads on the 3
coins flipped. To find the probabilities for each of the possible
outcomes, we will use the multiplication rule.
COIN 1
COIN 2
COIN 3
Probability
H
3 Heads: P(H) & PIH) & PIH) = 1/2- 1/2- 1/2= (1/2) = 1/8
1/2
2 Heads: P(H) & PIHO & P(T) = 1/2 - 1/2 - 1/2 = (/2 = 1/8
H12
H
2 Heads: P(H) & PIT) & PIH) = 1/2-1/2- 1/2 = (/2) = 1/8
1/2
1/2
H
T
2 Tails: PIH) & P(T) & PIT) = 1/2 - 1/2- 1/2 - (1/2) - 1/8
1/2
1/2
1/2
Start-
H
2 Heads: P(T) & P(H) & P(H) = 1/2- 1/2 - 1/2 = (/2) - 1/8
1/2
H.
1/2
1/2
1/2
2 Tails: P(T) & PIH) & PIT) = 1/2-1/2-1/2 - (1/2-1
= 1/8
1/2
H
2 Tails: PIT) & PIT) & PIH) = 1/2 - 1/2- 1/2 - (1/2 - 1/
1/2
т
3Tais: PIT) & PIT) & PIT) = 1/2- 1/2 - 1/2= (1/2) = 1/8
The sample space of the number of heads when three coins are tossed
is O heads (TTT), 1 head (HTT, THT,TTH), 2 heads (
HHT, THH, HTH), 3 heads (H HH). To find the probability of
each of the outcomes in this sample space, we will use the addition
rule. Example: P(1 head) = P(HTT or THT or
TTH) = ++ =
%3D
3
8
Heads, x
0 1 2 3
1
Probability, P(x) § § 8 8
3
Transcribed Image Text:Let's say we are interested in the probability number of heads on the 3 coins flipped. To find the probabilities for each of the possible outcomes, we will use the multiplication rule. COIN 1 COIN 2 COIN 3 Probability H 3 Heads: P(H) & PIH) & PIH) = 1/2- 1/2- 1/2= (1/2) = 1/8 1/2 2 Heads: P(H) & PIHO & P(T) = 1/2 - 1/2 - 1/2 = (/2 = 1/8 H12 H 2 Heads: P(H) & PIT) & PIH) = 1/2-1/2- 1/2 = (/2) = 1/8 1/2 1/2 H T 2 Tails: PIH) & P(T) & PIT) = 1/2 - 1/2- 1/2 - (1/2) - 1/8 1/2 1/2 1/2 Start- H 2 Heads: P(T) & P(H) & P(H) = 1/2- 1/2 - 1/2 = (/2) - 1/8 1/2 H. 1/2 1/2 1/2 2 Tails: P(T) & PIH) & PIT) = 1/2-1/2-1/2 - (1/2-1 = 1/8 1/2 H 2 Tails: PIT) & PIT) & PIH) = 1/2 - 1/2- 1/2 - (1/2 - 1/ 1/2 т 3Tais: PIT) & PIT) & PIT) = 1/2- 1/2 - 1/2= (1/2) = 1/8 The sample space of the number of heads when three coins are tossed is O heads (TTT), 1 head (HTT, THT,TTH), 2 heads ( HHT, THH, HTH), 3 heads (H HH). To find the probability of each of the outcomes in this sample space, we will use the addition rule. Example: P(1 head) = P(HTT or THT or TTH) = ++ = %3D 3 8 Heads, x 0 1 2 3 1 Probability, P(x) § § 8 8 3
Now use the histogram or table to answer the following questions.
1. What is the probability of flipping 3 coins and all three landing on
heads? P( H ) =
|(Enter your answer as a decimal. Do
not round.) HINT: Change the fraction to a decimal.
2. What is the probability of flipping 3 coins and getting 1 or 3
heads? P( H ) + + P( T) =
(Enter the outcomes in
numerical order. Enter your final answer only. Use the decimal
form of the probability. Do not round.)
3. What is the probability of flipping 3 coins and not getting 2
(Enter the final answer only. Use
heads? P(x + 2) = 6
decimal form of the probability. Do not round.)
Transcribed Image Text:Now use the histogram or table to answer the following questions. 1. What is the probability of flipping 3 coins and all three landing on heads? P( H ) = |(Enter your answer as a decimal. Do not round.) HINT: Change the fraction to a decimal. 2. What is the probability of flipping 3 coins and getting 1 or 3 heads? P( H ) + + P( T) = (Enter the outcomes in numerical order. Enter your final answer only. Use the decimal form of the probability. Do not round.) 3. What is the probability of flipping 3 coins and not getting 2 (Enter the final answer only. Use heads? P(x + 2) = 6 decimal form of the probability. Do not round.)
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