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Topic 879Unit 2 - UncertaintyBasic Probability Tools (cont.)Activity 8.3 Patterns in Multi-Flip Coin Experiments (cont.)(oc) alod ulded2 yI3. What would you expect in a 10-flip experiment? Try to quantify the following(aHow many outcomes will there be in the sample space of a 10-flip coin experiment? Explain.(b) How many different bars will there be in the probability distribution graph for this experiment(assuming that wekeep counting the number of heads as our outcome value)? Explain.(c) What is the probability that we get 0 heads in one run of our 10-flip coin experiment? Explain.(d) WhatExplain.the probability that we get 1 or more heads in one run of our 10-flip coin experiment?What is the probability that we get 0 or 1 heads in one run of our 10-clip coin experiment?Explain.4. Clearly, it's a little unreasonable to write out the sample space for a 10-flip coin experiment. Whenmathematicians reach a point where the most basic approach isn't realistic, they look for patterns thatmight lead to a formula for the quantity they are trying to count or measure. Indeed, such a formulaexists and it's been programmed into many different online calculators. It is called the binomialprobability formula because it calculates probabilities arising from random processes with only twooutcomes.:12t aoult r re:

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Its just the circled questions. Please help. Thanks in advance!!

Topic 8
79
Unit 2 - Uncertainty
Basic Probability Tools (cont.)
Activity 8.3 Patterns in Multi-Flip Coin Experiments (cont.)
(oc) alod ulded
2 yI
3. What would you expect in a 10-flip experiment? Try to quantify the following
(aHow many outcomes will there be in the sample space of a 10-flip coin experiment? Explain.
(b) How many different bars will there be in the probability distribution graph for this experiment
(assuming that we
keep counting the number of heads as our outcome value)? Explain.
(c) What is the probability that we get 0 heads in one run of our 10-flip coin experiment? Explain.
(d) What
Explain.
the probability that we get 1 or more heads in one run of our 10-flip coin experiment?
What is the probability that we get 0 or 1 heads in one run of our 10-clip coin experiment?
Explain.
4. Clearly, it's a little unreasonable to write out the sample space for a 10-flip coin experiment. When
mathematicians reach a point where the most basic approach isn't realistic, they look for patterns that
might lead to a formula for the quantity they are trying to count or measure. Indeed, such a formula
exists and it's been programmed into many different online calculators. It is called the binomial
probability formula because it calculates probabilities arising from random processes with only two
outcomes.
:12t aoult r re:
help_outline

Image Transcriptionclose

Topic 8 79 Unit 2 - Uncertainty Basic Probability Tools (cont.) Activity 8.3 Patterns in Multi-Flip Coin Experiments (cont.) (oc) alod ulded 2 yI 3. What would you expect in a 10-flip experiment? Try to quantify the following (aHow many outcomes will there be in the sample space of a 10-flip coin experiment? Explain. (b) How many different bars will there be in the probability distribution graph for this experiment (assuming that we keep counting the number of heads as our outcome value)? Explain. (c) What is the probability that we get 0 heads in one run of our 10-flip coin experiment? Explain. (d) What Explain. the probability that we get 1 or more heads in one run of our 10-flip coin experiment? What is the probability that we get 0 or 1 heads in one run of our 10-clip coin experiment? Explain. 4. Clearly, it's a little unreasonable to write out the sample space for a 10-flip coin experiment. When mathematicians reach a point where the most basic approach isn't realistic, they look for patterns that might lead to a formula for the quantity they are trying to count or measure. Indeed, such a formula exists and it's been programmed into many different online calculators. It is called the binomial probability formula because it calculates probabilities arising from random processes with only two outcomes. :12t aoult r re:

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check_circleAnswer
Step 1

Problems related to probability of events when 10 coins are tossed (flipped) , independently

Step 2

a) We may represent each of the 10 tosses by H (head) orT (tail). So each experiment can be described as a sequence of H or T (randomly) of length 10. So the total number of outcomes is 2^10=1024. (as each of the 10 places can be filled in 2 ways )

a)A typical outcome =
ΗΤΗΤΤΗΤΗΗΤ
(random sequence,length 10)
So, total number of outcomes
= 210 = 1024
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a)A typical outcome = ΗΤΗΤΤΗΤΗΗΤ (random sequence,length 10) So, total number of outcomes = 210 = 1024

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Step 3

(b) Denote the probability of Head as c; then the probability of 0-heads in a 10 -f...

b)Let Pr ob(H) -с,0 <c<1,
then Pr ob(T) -D1-с.
0-heads corresponds to
TTTTTTTTTT
(unique event)
So, P(0-heads)
— Р(TTTTTTTTTT)- Р(T)0 — (1- с)"°
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b)Let Pr ob(H) -с,0 <c<1, then Pr ob(T) -D1-с. 0-heads corresponds to TTTTTTTTTT (unique event) So, P(0-heads) — Р(TTTTTTTTTT)- Р(T)0 — (1- с)"°

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