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For the experiments in Exercises 13–18, write out the sample space S, choosing an S with equally likely outcomes, if possible. Then give the value of n(S) and tell whether the outcomes in S are equally likely. Finally, write the indicated events in set notation.

A coin is flipped until two heads appear, up to a maximum of four flips. (If three tails are flipped, the coin is still tossed a fourth time to complete the experiment).a. The coin is tossed four times.b. Exactly two heads are tossed.c. No heads are tossed.

(a) List outcomes of length $4 .$$\{\text { HTHH, TTHH, THTH, HTTH, TTTH, TTHT, THTT, HTTTY. }$(b) Outcomes with exactly $2 \mathrm{H} :$$\{\mathrm{HH}, \mathrm{THH}, \mathrm{~ H T H , ~ T T H H , ~ T H T H , ~ H T T H \} . ~}$(c) No heads-no "H' in the sequence:$\{\text { TTTTT }\}$

Calculus 2 / BC

Chapter 7

Sets and Probability

Section 3

Introduction to Probability

Sequences

Missouri State University

Campbell University

University of Nottingham

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04:03

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An experiment is conducted…

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Three coins are flipped. A…

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a. $\quad$ A balanced coin…

Okay, so we have slips. Number 2125 and two are drawn time scandalously so we can have a one and a two. I want one. Want to? We can't have a one and one because we draw two at once. So and there's only one simple fun. So we have one comment to one common three. One come before or one comma. Five. We can also have a to common one, not a two comma two. So that's to come with three to calm before and to come of five. Or we can have a three common one, three, comma two and we can't have a degree Common three. So basically, we can't have two numbers that are the same numbers for one for two, 43 count at 44 So 45 And lastly, we could have 51 52 five, three and 54 So this is our sample space. And for our first part report, they were asked to find, um when both ships are marked with even numbers. Okay, so I first wrote it didn't have even numbers. Our second roll. There's a two and a four. So that's an even number. We can also have see a four in it, too. But that's the same as two and four since where's Ah, swapping them around? So what's to say A is two comma four? Okay, Now for Part B, we have one. Slip is marked with the odd number, and the other is marked with an even number. Okay, so before I do that, let's remove the ones that have be Pete's. So it has to come before is the same as for comment, too. So we say one comma two is the same as two Company 31 Common three is the same as to become a one one come before is the same as for common. 115 is there was 5123 of the same is 32 25 or to foreign famous for 2 to 5 of the same. It's far too okay, and then we have 34 that status for three 35 That's the same as 53 and 45 is the same. It's five years to notice that we only have our upper, um, diagonal portion. Okay, so for part B, we wanted one step is marked with an odd and the other is more cute than even. So we see 12 That's odd. And even 13 is both hard won. Four is odd, and even when five is both odds, two and three is on and even two and four, that's both even two and five. That's odd and even, or even a nod. Something on 34 that's even in off and 35. That's both odd. 45 That's ought. And even so, we have 123456 We have one common to one come before to common. Three to come a five three com before and lastly, we have four come with five. Okay, And now for part C, we want both slips are marked with the same number. Well, actually, this is impossible, right? Cause we're drawn to simultaneously so we can't have 11 because we only have one slip with one. So that's just the empty set

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