Probability Tes...

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

No of heads	$$2$$	$$1$$	$$0$$
Frequency	$$200$$	$$550$$	$$250$$

Based on this information, the probability for at most one head is $$\dfrac{a}{b}$$, where $$(a,b)=1$$. Then $$\dfrac{a}{b}$$ is

There are $$500$$ packets in a large box and each packet contains $$4$$ electronic devices in it. On testing, at the time of packing, it was noted that there are some faulty pieces in the packets. The data is as below :

No. of faulty devices in a packet	Number of packets
$$0$$	$$300$$
$$1$$	$$100$$
$$2$$	$$50$$
$$3$$	$$30$$
$$4$$	$$20$$
Total number of packets	$$500$$

If one packet is drawn from the box, what is the probability that all the four devices in the packet are without any fault?

Fifty seeds were selected at random from each of $$5$$ bags $$A, B, C, D, E$$ of seeds, and were kept under standardised conditions equally favourable to germination. After $$20$$ days, the number of seeds which had germinated in each collection were counted and recorded as follow :

Bag	$$A$$	$$B$$	$$C$$	$$D$$	$$E$$
Number of seeds  germinated	$$40$$	$$48$$	$$42$$	$$39$$	$$41$$

What is the probability of germination of

$$(i)$$ more than $$40$$ seeds in a bag?

$$(ii)$$ $$49$$ seeds in a bag?

$$(iii)$$ more than $$35$$ seeds in a bag?

A tyre manufacturing company kept a record of the distance covered before a tyre needed to be replaced. The table show the result of $$1000$$ cases :

Distance in $$Km$$	Frequency
Less than $$4000$$	$$20$$
$$4000$$ to $$9000$$	$$210$$
$$9000$$ to $$14000$$	$$325$$
More than $$14000$$	$$445$$

If you buy a tyre of this company what is the probability that it will need to be replaced after it has covered somewhere between $$4000\, km$$ and $$14000\, km$$?

A survey was conducted by car manufacturing company in a metropolitan city on $$1000$$ persons having monthly income from Rs. $$30,001$$ to Rs. $$50,000$$. The data about the number of persons in various categories is as under:

Monthly income	Number of Cars
(in rupees)	$$1$$	$$2$$	More than $$2$$
$$30,001-40,000$$	$$400$$	$$50$$	$$25$$
$$40,001-50,000$$	$$100$$	$$300$$	$$125$$

 Find the probability that a person selected at random in the income slab $$40,001-50,000$$ have more than $$2$$ cars.

A couple of dice rolled. What is the empirical probability of getting the sum as $$5$$?

The record of a weather station shows that out of the past $$250$$ consecutive days, its weather forecasts were correct $$175$$ times. What is the probability that on a given day it was correct?

A box has tokens numbered $$3$$ to $$100$$. If a token is taken out at random the chance that the number is divisible by $$7$$ is

You have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector,  if the probability of getting a non-blue sector is $$\dfrac{4}{m}$$. Then, the  value of $$m$$ is 

A box contains $$32$$ coloured marbles. $$8$$ of them are red marbles and the rest are either blue or green marbles. A marble is drawn at random. Calculate the probability of drawing a marble which is not red in colour.