Probability

Direction: A bag contains $4$ red, $5$ brown and $6$ white balls. Three balls are drawn randomly:

What is the probability that balls drawn contains exactly two red balls?

Direction: A bag contains $4$ red, $5$ brown and $6$ white balls. Three balls are drawn randomly:

What is the probability that the balls drawn are not of the same colour?

A ball is thrown at a circular bin such that it will land randomly over the area of the bin. Find the probability that it lands closer to the centre than to the edge?

A five letter word is formed using the letters P, R, I, M and E (repetition is not allowed). Find the probability of getting a word in which the consonants should not be together.

 A bag contains $6$ red ball, $4$ blue, $2$ green ball and $3$ yellow ball. If four balls are picked at random what is the probability that one is green, two are blue and one is red? 

The bag $\mathrm{A}$ contains $5$ blue and $6$ red balls, bag $\mathrm{B}$ contains $7$ blue and $5$ red balls. If $6$ balls are drawn at random from each of the bags, find the product of the probability that $4$ blue and $2$ red balls are drawn from bag $\mathrm{A} \mathrm{and} 3$ blue and $3$ red balls are drawn from bag $\mathrm{B}$.

A bag contains $6$ blue balls, $5$ red balls, and $7$ green balls, if two balls selected, what is the probability of not selecting same colour ball?

A bag contains $4$ green, $5$ blue and $6$ black balls. Three balls are drawn at random from the bag. Find the probability that at most $2$ balls are blue ball :

A bag contains four blue shirts and three black shirts. If three shirts drawn random from bag what is the probability that two blue and one black?

There are two bags $\mathrm{A} \mathrm{and} \mathrm{B}$. Bag $\mathrm{A}$ contains $5$ blue balls and $x$ red balls and bag $\mathrm{B}$ contains $x$ blue balls and $8$ red balls. If one ball is chosen at random from any one bag then the probability that it is a red ball is $\frac{5}{9}$. Which of the following can be the value of $x?$

$$\begin{gathered} \mathrm{I}. 10 \\ \mathrm{II}. 4 \\ \mathrm{III}. 3 \\ \mathrm{IV}. 5 \\ \mathrm{V}. 6 \end{gathered}$$

What is the probability that three cards are taken out will King from the pack of $52$ cards?

There are $6$ pens and $4$ pencils in a bag. If any four items are chosen at random, then what is the probability that they must have atlest one pencil?

Card numbers from $1, 3, 5, 7, 9..... 33$ are put in a bag. A card is drawn from it at random. Find the probability that the number on the card is not divisible by $3$ or divisible by $2$?

The chance that Om can solve a certain problem is $\frac{1}{4}$, the chance that Jay can solve it is $\frac{2}{3}$.Find the probability that the problem is solved if they both try:

If the winning percentage probability of Australia is 60%. Find out the probability in favour of Winning Australia?

A TV weather presenter says that there is not much chance of rain tomorrow. Which percentage best describes the probability? 

A painter paints six faces of a cubical room with six completely different colours red, blue, pink, yellow, green and orange. What's the chance that red, pink and blue faces share a standard corner?

In a bag the number of pink, red and yellow ball is $2x, 5x \& 8x$, respectively. If two balls are taken out randomly, the probability of getting exact $2$ yellow balls is $\frac{46}{165}$, then which of the following can be found from the given information?

$\left(\mathrm{i}\right)$ The total number of pink and red balls in the bag.

$\left(\mathrm{ii}\right)$ The probability of getting $2$ pink and $1$ yellow ball.

$\left(\mathrm{iii}\right)$ The number of yellow balls.

The question consists of three statements numbered “I, II and III” given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. There are cubes of three different types ‘A’, ‘B’ and ‘C’ in a bag. Find the number type ‘B’ cubes.

Statement I: The probability of picking a type ‘B’ cube is $\frac{1}{3}$.

Statement II: The number of type ‘A’ cubes is more than that of type ‘C’ cubes

Statement III: The ratio of the number of type ‘A’ cube that of type ‘C’ cube is $2:1$.

A bag $\left(X\right)$ contains some red balls and some green balls, and their respective ratio is $4 : 5$. If three more red balls are added and one green ball is taken out from bag then the new ratio of red balls to green balls become $11 : 9$.

If $\text{'}n\text{'}$ number of blue balls are added in bag $\left(X\right)$ and one ball is taken from the bag, then the probability of getting either blue or red is $\frac{2}{3}$. Find $\text{'}n\text{'}$.