Question

an unfair coin with pr[tails]= .15 is flipped 6 times. what is the probability of getting EXACTLY 1 tail in the 6 flips?

Answer 1

done, see your previous post

Answer 2

it's two different questions (:

Answer 3

I assumed you could make the tiny adjustment.

prob(exactly 1T) = C(5,1) (.15)^1 (.85)^4
=

Answer 4

Thank you so much

Answer 5

Abigail flipped a coin 100 times and 47 of the 100 flips were tails. She wanted to see how likely a result of 47 tails in 100 flips would be with a fair coin, so Abigail used a computer simulation to see the proportion of tails in 100 flips, repeated 100 times. Based on the results of the simulation, what inference can Abigail make regarding the fairness of the coin?
Proportion of Tails Flipped
0.35
0.4
0.45
0.5
0.55
0.6
0.65


(Note: don't use percents as a sample proportion.)

Since the simulation shows
with a sample proportion of
or
, we can conclude that
.

Answer 6

Since Abigail simulated a fair coin 100 times, the proportion of tails flipped should be around 0.5. However, the proportion of tails she observed was 0.47. Looking at the simulation results, the proportion of tails varies from 0.35 to 0.65, which suggests that it is possible to observe proportions different from 0.5 due to chance alone, even with a fair coin. Therefore, based on the simulation results, Abigail cannot make a clear inference about the fairness of the coin.

Answer 7

Hailey rolled a die 50 times and 15 of the 50 rolls came up as a six. She wanted to see how likely a result of 15 sixes in 50 rolls would be with a fair die, so Hailey used a computer simulation to see the proportion of sixes in 50 rolls, repeated 200 times. Based on the results of the simulation, what inference can Hailey make regarding the fairness of the die?
Proportion of Sixes Rolled
0
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
0.36


(Note: don't use percents as a sample proportion.)

Since the simulation shows
with a sample proportion of
or
, we can conclude that
.

Answer 8

Since Hailey simulated a fair die 200 times, the proportion of sixes rolled should be around 1/6, which is approximately 0.167. However, the proportion of sixes she observed was 15/50, which is 0.3. Looking at the simulation results, the proportion of sixes varies from 0 to 0.36, but none of the proportions are as high as 0.3, which suggests that it is unlikely to observe such a high proportion of sixes due to chance alone with a fair die. Therefore, based on the simulation results, Hailey can suspect that the die she rolled might not be fair, and further investigation may be needed.

Answer 9

Sydney rolled a die 40 times and 0 of the 40 rolls came up as a six. She wanted to see how likely a result of 0 sixes in 40 rolls would be with a fair die, so Sydney used a computer simulation to see the proportion of sixes in 40 rolls, repeated 200 times. Based on the results of the simulation, what inference can Sydney make regarding the fairness of the die?
Proportion of Sixes Rolled
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35


(Note: don't use percents as a sample proportion.)

Since the simulation shows
with a sample proportion of
or
, we can conclude that

Answer 10

since the sample proportion of sixes in the 40 rolls Sydney made was 0, it is highly unlikely to get such a result due to chance alone with a fair die. Looking at the simulation results, the proportion of sixes varies from 0 to 0.35, but none of the proportions are as low as 0, which reinforces the idea that getting 0 sixes in 40 rolls is an unusual event. Therefore, based on the simulation results, Sydney may suspect that the die she rolled might not be fair, and further investigation may be needed.