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?

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:

What is the probability of getting $5$ heads when you toss a coin $10$ times?

If a six-sided dice is rolled $10$ times, then find the binomial Probability of rolling a $2$ on $3$ trials and others on the remaining trials,

Six coins are tossed simultaneously. The probability that at least one head turning up, is:

In a box containing $100$ bulbs, $10$ are defective, $10$ bulbs are chosen randomly from this box. The probability that exactly $4$ of the chosen bulbs are defective :

A fair coin is tossed a fixed number of times. If the probability of getting six heads is equal to that of getting of eight heads, then what is the total number of tosses? 

On a bookshelf there are $40\%$ fictional and the rest are non fictional books. If $25\%$ of the fictional books have red cover and $10\%$ of the non fictional books have red cover, find the probability that a red cover book selected at random is not a fictional book :

Find the probability that the marble is neither red nor white when a random marble is drawn from a bag containing $7$ red, $5$ blue, $4$ white and $4$ black marbles :

There are $3$ similar boxes, containing
(i) $16$ red and $14$ orange balls;
(ii) $13$ red and $17$ orange balls, and
(iii) $15$ red and $15$ orange balls, severally.
If you select one amongst the $4$ boxes randomly and from that exact box acquire a ball randomly and realise that it be red, what's the chance that the ball was picked up from the second box$?$

There are $5$ red balls, $4$ yellow balls and $3$ green balls in a basket. If $3$ balls are drawn at random, what is the probability that at least $2$ of them are green in colour?

A bag contains $12$balls (red and blue). Two balls are drawn randomly from the bag and the probability of one ball being red and one ball being blue is $\frac{35}{66}$. If ‘n’ blue balls are added to the bag and then two balls are taken out randomly, then the minimum probability of remaining blue balls in the bag is $\frac{9}{14}$. Find the value of ‘n’, provided that blue balls are more than the red balls in the bag initially.

If two dice A and B are rolled simultaneously, what is the probability that the number appearing on the top faces of the dice A is a multiple of the number appearing on the top faces of the dice B and vice versa?

Find the probability of choosing a team of $11$players from $8$batsmen and $8$bowlers if it is given that the number of batsmen should always be greater than the number of bowlers.

Direction - Solve the Question:

There are $5$ red, $6$ black and $5$ blue balls in a bag. Out of these balls, four balls are picked at random from the bag. Then, what is the probability that one is red, two are black and one is the blue ball?

There are $8$ green and $4$ red balls. If $2$ balls are withdrawn, then what is the probability that at least one of the balls withdrawn will be red?

There are three similar boxes, containing

(i) $6$black and $4$ white balls;

(ii) $3$ black and $7$ white balls and

(iii) $5$ black and $5$ white balls, respectively.

If you choose one of the three boxes at random and from that particular box pick up a ball at random and find that to be black, what is the probability that the ball was picked up from the second box?