Question 1 :
A coin is tossed $400$ times and the data of outcomes is below:<span class="wysiwyg-font-size-medium">&#160;<span class="wysiwyg-font-size-medium"><br/><table class="wysiwyg-table"><tbody><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Outcomes&#160;</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$H$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$T$</p></td></tr><tr><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">Frequency</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$280$</p></td><td><span class="wysiwyg-font-size-medium"><br/> <p class="wysiwyg-text-align-center">$120$</p></td></tr></tbody></table><p><br/></p><p>Find:</p><p>(i) $P(H)$, i.e., probability of getting head</p><p>(ii) $P (T)$, i.e., probability of getting tail.&#160;</p><p>(iii) The value of $P (H) + P (T)$.</p>

Question 2 :
Ticket numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5 ?

Question 3 :
The probability of guessing the correct answer to a certain test is $\displaystyle\frac{x}{2}$. If the probability of not guessing the correct answer to this questions is $\displaystyle\frac{2}{3}$, then $x$ is equal to ______________.

Question 4 :
A pair of dice is thrown once The probability that the sum of the outcomes is less than 11 is

Question 5 :
What is the maximum value of the probability of an event?

Question 6 :
If the probability of the occurrence of an event is P then what is the probability that the event doesn't occur.

Question 8 :
Out of the digits $1$ to $9$, two are selected at random&#160;and one is found to be $2$, the probability that their&#160;sum is odd is

Question 9 :
If $P(A) = \dfrac{5}{9}$, then the odds against the event $A$ is

Question 10 :
A bag contains 5 blue and 4 black balls. Three balls are drawn at random. What is the probability that 2 are blueand 1 is black?

Question 11 :
A fair dice has faces numbered $0, 1, 7, 3,&#160;5$ and $9$. If it is thrown, the probability of&#160;getting an odd number is

Question 12 :
A biased coin with probability $p , 0 &lt; p &lt; 1 ,$ of heads is tossed until a head appears for thefirst time. If the probability that the number of tosses required is even, is $2 / 5 ,$ then $p$ equal to

Question 13 :
If the events $A$ and $B$ mutually exclusive events such that $P(A)=\dfrac {1}{3}(3x+1)$ and $P(B)=\dfrac {1}{4}(1-x)$, then the aet of possible values of $x$ lies in the interval:

Question 14 :
A pair of dice is thrown. Find the probability of getting a sum of $8$ or getting an even number on both the dices.

Question 15 :
One hundred identical coins each with probability p as showing up heads are tossed. If $0 &lt; p &lt; 1$ and the probability of heads showing on 50 coins is equal to that of heads on 51 coins, then the value of p is

Question 17 :
Vineeta said that probability of impossible events is $1$. Dhanalakshmi said that probability of sure events is $0$ and Sireesha said that the probability of any event lies between $0$ and $1$.<br>in the above, with whom will you agree?

Question 19 :
The probability of an event $A$ lies between $0$ and $1$, both inclusive. Which mathematical expression best describes this statement?<br/>

Question 20 :
According to the property of probability, $P(\phi) = 0$ is used for <br>

Question 21 :
Two dice are thrown. Find the odds in favour of getting the sum $4$.<br/>

Question 22 :
If I calculate the probability of an event and it turns out to be $7$, then I surely know that<br/>

Question 23 :
A game of chance consists of spinning an arrow which is equally likely to come to rest pointing to one of the number between 1 to 15. What is the probability that it will point to an odd number.

Question 25 :
A bulb is taken out at random from a box of 600 electricbulbs that contains 12 defective bulbs. Then theprobability of a non-defective bulb is

Question 27 :
.................&#160;states the possibility of the prime factorization of any natural number is unique. The numbers can be multiplied in any order.

Question 28 :
Use Euclid's division lemma to find the HCF of the following<br/>16 and 176

Question 31 :
Euclids division lemma, the general equation can be represented as .......

Question 32 :
State whether the following statement is true or false.The following number is irrational<br/>$6+\sqrt {2}$

Question 33 :
If $a=\sqrt{11}+\sqrt{3}, b =\sqrt{12}+\sqrt{2}, c=\sqrt{6}+\sqrt{4}$, then which of the following holds true ?<br/>

Question 35 :
A rectangular veranda is of dimension $18$m $72$cm $\times 13$ m $20$ cm. Square tiles of the same dimensions are used to cover it. Find the least number of such tiles.

Question 36 :
Euclids division lemma can be used to find the $...........$ of any two positive integers and to show the common properties of numbers.

Question 39 :
The LCM of 54 90 and a third number is 1890 and their HCF is 18 The third number is

Question 40 :
If $a=107,b=13$ using Euclid's division algorithm find the values of $q$ and $r$ such that $a=bq+r$