Probability Tes...

If we throw a dice, then the sample space, $$S = {1, 2, 3, 4, 5, 6}$$. Now the event of $$3$$ appearing on the dice is simple and given by

Xavier, Yvonne, and Zelda each try independently to solve a problem. If their individual probabilities for success are $$\displaystyle \frac { 1 }{ 4 } ,\frac { 1 }{ 2 } $$ and $$\displaystyle \frac { 5 }{ 8 } $$, respectively, what is the probability that Xavier and Yvonne, but not Zelda, will solve the problem?

A coin is tossed $$100$$ times with the following frequencies: Head : $$20$$. Find the probability for event having heads only.

Difference between sample space and subset of sample space is considered as

Two coins are available, one fair and the other two-headed. Choose a coin and toss it once; assume that the unbiased coin is chosen with probability $$\dfrac {3}{4}$$. Given that the outcome is head the probability that the two-headed coin was chosen, is

Which of the following is true regarding law of total probability?

A bag contains three red balls and two blue balls. We remove successively, and with replacement, two balls and observe their colour. What is the probability of "to extract a red ball and a blue one, without taking into account the order"?

Let $$S$$ be a set containing $$n$$ elements and we select two subsets $$A$$ and $$B$$ of $$S$$ at random, then the probability that $$A\cup B=S$$ and $$A\cap B=\phi$$, is.

There are two coins, one unbiased with probability $$\cfrac{1}{2}$$ of getting heads and the other one is biased with probability $$\cfrac{3}{4}$$ of getting heads. A coin is selected at random and tossed. It shows heads up. Then, the probability that the unbiased coin was selected is

I have three bags that each contain $$100$$ marbles- Bag $$1$$ has $$75$$ red and $$25$$ blue marbles, Bag $$2$$ has $$60$$ red and $$40$$ blue marbles, Bag $$3$$ has $$45$$ red and $$55$$ blue marbles. I choose one of the bags at random and then pick a marble from the chosen bag, also at random. What is the probability that the chosen marble is red?