Probability Tes...

A group of boys and girls know either English or Hindi. The number of boys and girls are in the ratio 1:4 given 30% of girls know Hindi and the rest of them know English. On other hand, 50% of the boys know Hindi and the rest of them know English. A student chosen at random from the group of student knows Hindi, the probability that the chosen student was a girl is

If the range of a random variable $$X$$ is $${0,\ 1,\ 2,\ 3,....}$$ with $$P{X=K}=\dfrac {(k+1)a}{3^{k}}$$ for $$k\ge 0$$, then $$a=$$  

There are 5 students S1,S2,S3,S4,S5 in a music class and for them there are 5 seats in a row. On examination day, all five students are randomly allotted the five seats. Let Ti denote the event that Si and Si+1 do NOT sit adjacent to each other on examination day. (i=1,2,3,4) What is the probability that T1,T2,T3,T4,T5 all occur simultaneously on examination day? If the probability is of the form A/B, find A+B

A dice is thrown twice and the sum of the numbers appearing is observed to be $$6$$ . What is the conditional probability that the number $$4$$ has appeared at least once?

The c.d.f of a discrete r.v X isThen $$P\left(X=-3|X<0\right)$$

Lot A consist of 3G and 2D articles. Lot B consists of 4G and 1D article, A new lot C is formed by taking 3 articles from A and 2 from B. The probability that an article chosen at random from C is defective, is

Two coins are tossed 1000 times and the outcomes are recorded as below:

There are eight machines and it is known that exactly three of them are faulty. They are tested, one-by-one, in a random order till all the faulty machines are identified. Then the probability that only three tests are needed is 

A sample of 4 items is drawn at random with replacement from a lot of 10 items containing 3 defective items. If $$  X  $$ denotes the number of defective items in the sample, then $$  P(0<X<3)= $$

A sample of 4 items is drawn at random with replacement from a lot of 10 items containing3 defective items. If $$X$$ denotes the number of defective items in the sample, then $$P ( 0 < X < 3 ) =$$