Answer: Our required probability is 0.83.
Step-by-step explanation:
Since we have given that
Number of dices = 2
Number of fair dice = 1
Probability of getting a fair dice P(E₁) = 
Number of unfair dice = 1
Probability of getting a unfair dice P(E₂) = 
Probability of getting a 3 for the fair dice P(A|E₁)= 
Probability of getting a 3 for the unfair dice P(A|E₂) = 
So, we need to find the probability that the die he rolled is fair given that the outcome is 3.
So, we will use "Bayes theorem":

Hence, our required probability is 0.83.
Answer:
yes they form a proportion
Answer:
x > 24
Step-by-step explanation:
12 + 12 = 24
Step-by-step explanation:
Answer is in the pic above
Answer:
The required confidence inteval = 94.9%.
Step-by-step explanation:
Confidence interval: Mean ± Margin of error
Given: A confidence interval for the true mean diameter of all oak trees in the neighbourhood is calculated to be (36.191, 42.969).
i.e. Mean + Margin of error = 42.969 (i)
Mean - Margin of error = 36.191 (ii)
Adding (i) and (ii), we get

Margin of error = 42.969-39.58 [from (i)]
= 3.389
Margin of error = 
here n= 25 
i.e.

Using excel function 1-TDIST.2T(2.054,24)
The required confidence inteval = 94.9%.