F(1)=P(X ≤ 1)
P(X ≤ 1) = P(X=1) + P(X=0)
= 1/2 + 1/8
= 5/8

The probability of coin landing on tail = \(\frac {1}{2}\)
The probability of dice showing 2 = \(\frac {1}{6}\)
Total probability = \(\frac {1}{2} \times \frac {1}{6} = \frac {1}{12}\)

In Bayesian statistics, we calculate new probability after information becomes available due to new events and this is known as Posterior Probability. There is no term like Independent probabilities and Dependent probabilities, re are only independent events and dependent events. Interior probabilities represent probabilities of intersection between two events.

Yellow color ball is not listed in question. The bag contains only red, white and green color balls. So, probability to draw a yellow color ball out of bag is zero.

We know that P(A|B) = P(A∩B) / P(B). (By formula for conditional probability)
The value of P(B) = 0 in given question. As value of denominator becomes 0, value of P(A|B) becomes un-defined.

A random experiment that has only two mutually exclusive outcomes called ?success? and ?failure?. This experiment is called a Dichotomous experiment and is repeated n times. So, it is called as Bernoulli trials.

Bernoulli trials is termed after swiss mamatician Jacob Bernoulli. Bernoulli trials is also called a Dichotomous experiment and is repeated n times. If in each trial probability of success is constant, n such trials are called Bernoulli trails.

Total number of balls = 4 + 7 = 11
The probability of first ball to be red = \(\frac {4}{11}\)
The probability of drawing blue ball as second ball out with replacement = \(\frac {7}{11}\)

Probability of yellow = \(\frac {1}{5}\)
Probability of choosing pink pair of gloves twice = \(\frac {1}{5} \times \frac {1}{5} = \frac {1}{25}\)

Possible outcomes when a dice is thrown = {1, 2, 3, 4, 5, 6}
Multiples of 3 = {3, 6}
Total probability = \(\frac {number \, of \, multiples \, of \, 3}{number \, of \, possible \, outcomes} = \frac {2}{6}=\frac {1}{3}\)