Question

At the recently opened theme park, Six Samples Over a Population, a carnival game allows a player three attempts, using a dart, to pop a balloon. As soon as the player pops the balloon, he wins the prize and the game is over. If he does not pop the balloon after the third attempt he loses. Niloy, an avid dart-throwing balloon popper, estimates his probability of popping the balloon on the first attempt at 20%, popping the balloon on the second attempt at 30%, and popping the balloon on the third attempt at 40%. By describing an appropriate random digit assignment and performing 10 simulations using the given random number table, determine the probability that Niloy wins the prize.

0 8 4 2 4 4 4 7 5 3 7 7 3 7 7 2 8 7 4 4 7 5 5 9 2 0 8 5 6 3 7 9 1 4 0 9 2 4 5 4
5 3 6 4 5 6 6 8 1 2 6 1 4 2 1 4 7 8 3 6 1 2 6 0 9 1 5 3 7 3 9 8 4 8 1 1 4 5 9 2

Answer 1

@jim_thompson5910

Answer 2

hmm let me think

Answer 3

okay

Answer 4

we have the numbers 0 through 9

basically 10 single digits

if we say "picking 0 or 1 means you win", then that's the same as saying "you have a 20% chance of winning" since there are 2 numbers to pick that give you a winner out of 10 total.

Agreed?

Answer 5

yes

Answer 6

so I guess based off that logic, and the fact that 0 is first in that long list of numbers (given up top), he wins on the first try

that seems kinda boring, so let's flip things. Let's make it like this

Rule: if you get 8 or 9, you win. Otherwise, you lose. We will start with 0 and count up to 9

Answer 7

okay

Answer 8

hmm wait, I might be getting ahead of myself

Answer 9

does it specify the instructions on what consists of a win or not?

Answer 10

ex: does it say "0 or 1 means win" ?

Answer 11

no it doesn't

Answer 12

hmm then I'm not sure how to proceed

Answer 13

I guess I could make something up, but if it doesn't agree with the teacher, then it won't work

Answer 14

its an online class so my teacher doesn't really specify as to what or how to learn something i have to pretty much learn on my own

Answer 15

ok then I guess there's not much else we can do but make up the rules a bit here

Answer 16

thats fine

Answer 17

For the 20% chance (first try)
Rule: picking a 0 or 1 means you win. Picking anything else means you lose.


For the 30% chance (second try)
Rule: picking a 0, 1, or 2 means you win. Picking anything else means you lose.


For the 40% chance (third try)
Rule: picking a 0, 1, 2, or 3 means you win. Picking anything else means you lose.

Answer 18

now we look at this string of numbers

0 8 4 2 4 4 4 7 5 3 7 7 3 7 7 2 8 7 4 4 7 5 5 9 2 0 8 5 6 3 7 9 1 4 0 9 2 4 5 4
5 3 6 4 5 6 6 8 1 2 6 1 4 2 1 4 7 8 3 6 1 2 6 0 9 1 5 3 7 3 9 8 4 8 1 1 4 5 9 2

Answer 19

based on that string, do we win on the first try?

Answer 20

yes

Answer 21

good

Answer 22

that will be considered simulation 1

make a note somewhere that simulation1 ends with a win in one try

Answer 23

simulation1: win (first try)

Answer 24

now we erase that first 0 in the string of numbers and look to the next number: 8

and we start the simulation over again. Do we win on the first try?

Answer 25

no

Answer 26

good, because we didn't get a 0 or 1 on the first try

do we win on the second try?

Answer 27

still no

Answer 28

yep, 4 isn't 0 or 1 or 2

how about the third try?

Answer 29

still no:)

Answer 30

why not?

Answer 31

oh wait i thought we were still on 4 but its 2 now so the answer is yes

Answer 32

yeah that '2' is in the group "0,1,2,3" since we're on attempt #3

so we win on the third try

Answer 33

okay

Answer 34

simulation1: win (first try)
simulation2: win (third try)

Answer 35

so we have

0 8 4 2 4 4 4 7 5 3 7 7 3 7 7 2 8 7 4 4 7 5 5 9 2 0 8 5 6 3 7 9 1 4 0 9 2 4 5 4
5 3 6 4 5 6 6 8 1 2 6 1 4 2 1 4 7 8 3 6 1 2 6 0 9 1 5 3 7 3 9 8 4 8 1 1 4 5 9 2

and we've used up the numbers 0,8,4,2 of that table to do simulation 1 and simulation 2

scratch them out and you'll have '4' as the first number that isn't scratched out. That will be the starting number for simulation 3

Answer 36

repeat the steps to carry out simulation 3 and tell me what you get

Answer 37

okay so stimulation 3: win (fourth try)?

Answer 38

you only get 3 attempts (not 4)

Answer 39

so then stimulation 3: not win?

Answer 40

Attempt 1: 4 --> loss (since we need 0 or 1)
Attempt 2: 4 --> loss (since we need 0 or 1 or 2)
Attempt 3: 4 --> loss (since we need 0 or 1 or 2 or 3)

overall,

Simulation3: loss

Answer 41

simulation1: win (first try)
simulation2: win (third try)
simulation3: loss

Answer 42

yes thats what i got as well

Answer 43

so you're basically doing this until you have done 10 simulations

Answer 44

oh okay so can i do the 6 remaining, and have you approve or deny it?

Answer 45

This is probably a succinct way to express how to you got your sub-answers to the teacher.

Simulation 4:

Numbers from the random number table we'll use: 7 5 3

Attempt 1: 7 --> loss (since we need 0 or 1)
Attempt 2: 5 --> loss (since we need 0 or 1 or 2)
Attempt 3: 3 --> win (since we need 0 or 1 or 2 or 3)

overall,

Simulation4: win (third try)

Answer 46

simulation1: win (first try)
simulation2: win (third try)
simulation3: loss
simulation4: win (third try)

and so on...

Answer 47

so can i do the rest and have you check my work?

Answer 48

yes that sounds like a good plan

Answer 49

okay just give me a moment

Answer 50

alright, in the meantime, I'll be right back

Answer 51

stimulation5: win (third try)
attempt 1: 7 loss (since we need 0 or 1)
attempt 2: 7 loss (since we need 0, 1, or 2)
attempt 3: 3 win (since we need 0, 1, 2, or 3)

Answer 52

stimulation6: win (third try)
attempt 1: 7 loss (since we need 0 or 1)
attempt 2: 7 loss (since we need 0, 1, or 2)
attempt 3: 2 win (since we need 0, 1, 2, or 3)

Answer 53

stimulation 7: loss
attempt 1: 8 loss (since we need 0 or 1)
attempt 2: 7 loss (since we need 0, 1, or 2)
attempt 3: 4 loss (since we need 0, 1, 2, or 3)

Answer 54

stimulation 8: loss
attempt 1: 4 loss (since we need 0 or 1)
attempt 2: 7 loss (since we need 0, 1, or 2)
attempt 3: 5 loss (since we need 0, 1, 2, or 3)

Answer 55

stimulation 9: win (third try)
attempt 1: 5 loss (since we need 0 or 1)
attempt 2: 9 loss (since we need 0, 1, or 2)
attempt 3: 2 win (since we need 0, 1, 2, or 3)

Answer 56

stimulation 10: win (first try)
attempt 1: 0 win (since we need 0 or 1)
attempt 2:
attempt 3:

Answer 57

@jim_thompson5910 im done

Answer 58

@jim_thompson5910

Answer 59

very good, so we have this complete picture of the 10 simulations

simulation1: win (first try)
simulation2: win (third try)
simulation3: loss
simulation4: win (third try)
stimulation5: win (third try)
stimulation6: win (third try)
stimulation 7: loss
stimulation 8: loss
stimulation 9: win (third try)
stimulation 10: win (first try)

I've attached a visual way to look at it

Answer 60

we have 3 losses (simulation3,simulation7,simulation8)

the rest are wins

so we have 10-3 = 7 wins out of 10 total

the probability he wins is 7/10

Answer 61

okay great :) is that it?

Answer 62

yes it is

Answer 63

okay thank you so much!!!

Answer 64

np