Answer:
left limit = 2 ≠ 1/2 = right limit
Step-by-step explanation:
A function is discontinuous if the limit of the function value approaching the point from the left is different than the limit approaching from the right.
Here, the left limit is 2 and the right limit is 1/2. The limits are different, which is why the function is discontinuous at x=-1.
Answer:
the probability the die chosen was green is 0.9
Step-by-step explanation:
Given that:
A bag contains two six-sided dice: one red, one green.
The red die has faces numbered 1, 2, 3, 4, 5, and 6.
The green die has faces numbered 1, 2, 3, 4, 4, and 4.
From above, the probability of obtaining 4 in a single throw of a fair die is:
P (4 | red dice) =
P (4 | green dice) = =
A die is selected at random and rolled four times.
As the die is selected randomly; the probability of the first die must be equal to the probability of the second die =
The probability of two 1's and two 4's in the first dice can be calculated as:
=
=
=
=
=
=
The probability of two 1's and two 4's in the second dice can be calculated as:
=
=
=
=
=
∴
The probability of two 1's and two 4's in both dies = P( two 1s and two 4s | first dice ) P( first dice ) + P( two 1s and two 4s | second dice ) P( second dice )
The probability of two 1's and two 4's in both die =
The probability of two 1's and two 4's in both die =
The probability of two 1's and two 4's in both die =
By applying Bayes Theorem; the probability that the die was green can be calculated as:
P(second die (green) | two 1's and two 4's ) = The probability of two 1's and two 4's | second dice)P (second die) ÷ P(two 1's and two 4's in both die)
P(second die (green) | two 1's and two 4's ) =
P(second die (green) | two 1's and two 4's ) =
P(second die (green) | two 1's and two 4's ) = 0.9
Thus; the probability the die chosen was green is 0.9