Alison is learning how to walk. 50% of the time that she takes a step she falls down. Her older brother wants to design a simulation to find the probability she will fall down 5 out of the next 7 times she tries to take step.
Which simulation design has an appropriate device and a correct trial?
Answers
Answer:
Answer with explanation:
Alison is learning how to walk.50% of times she takes a step she falls down.
Probability of falling down in next step =\frac{50}{100}=\frac{1}{2}=
100
50
=
2
1
Probability of not falling down in next step =\frac{50}{100}=\frac{1}{2}=
100
50
=
2
1
From ,the four option given,we have to find the best simulation which her older brother wants to design a simulation to find the probability that she will fall down 5 out of the next 7 times she tries to take step.
While Simulating the Probability of falling down should be =\frac{5}{7}=
7
5
And , probability of not falling down1-\frac{5}{7}=\frac{2}{7}1−
7
5
=
7
2
→→⇒F=Falling, NF=Non Falling
A) Roll a die letting 1 represent Alison falling and 2-6 represent Alison not falling. Roll the die five times.
P(F)=\frac{1}{6},P(NF)=\frac{5}{6}P(F)=
6
1
,P(NF)=
6
5
Incorrect option,probabilities of falling and non falling does not match with Actual probability of falling and non falling.
B) Roll a die letting 1 represent Alison falling and 2-6 represent Alison not falling. Roll the die seven times.
P(F)=\frac{1}{6},P(NF)=\frac{5}{6}P(F)=
6
1
,P(NF)=
6
5
Incorrect option,probabilities of falling and non falling does not match with Actual probability of falling and non falling.
C) Let Heads represent Alison falling down and Tails representing Alison not falling down. Flip the coin five times.
P(F)=\frac{1}{2},P(NF)=\frac{1}{2}P(F)=
2
1
,P(NF)=
2
1
Simulation is done only five times , that is coin has been flipped only five times.it must have been flipped seven times.Incorrect option.
D) Let Heads represent Alison falling down and Tails representing Alison not falling down. Flip the coin seven times.
P(F)=\frac{1}{2},P(NF)=\frac{1}{2}P(F)=
2
1
,P(NF)=
2
1
Simulation is done seven times , that is coin has been flipped seven times.So,she should fall 5 times that is head should appear 5 out of seven times, and tail should appear 2 out of seven times.correct option.
Option D
Step-by-step explanation:
Simulation <--> (corresponds to) Real world as follows
Flip of coin <--> Alison tries to take a step
"Flip the coin 7 times" <--> "the next 7 times she tries to take a step"
Heads <--> Alison falls down
50% probability of heads <--> 50% of the time she takes a step she falls
Notice that:
probability of 5 heads in 7 tosses <--> probability of 5 falls in 7 steps
so to investigate the probability of Alison falling down 5 out of the next 7 times she tries to take a step, the brother will need to look at the probability of getting 5 heads in 7 tosses in his simulation.