1 Marks Question

Question 11 Mark

A number is chosen at random from the numbers $-3,-2,-1,0,1,2,3$. What will be the probability that square of this number is less than or equal to $1 ?$

Answer

Here, the sample space $S$ is
$S=\{-3,-2,-1,0,1,2,3\}$
And, the favourable outcomes $E$ is $E =\{-1,0,1\}$
$\therefore P(E)=\frac{\text { Number of elements in } E}{\text { Number of elements in } S}$
$\Rightarrow P(E)=\frac{3}{7}$
Hence, the probability of getting a number whose
square is less than or equal to $1$ is $\frac{3}{7}$.

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Question 21 Mark

Cards marked with number $3,4,5, \ldots ., 50$ are placed in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the selected card bears a perfect square number.

Answer

It is given that the box contains cards marked with numbers $3,4,5, \ldots ., 50$
Therefore, the total number of outcomes $=48$
The perfect squares between numbers $3$ and $50$ are $4,9,16,25,36$ and $49 .$
So, the number of favourable outcomes $=6$
Hence, the probability that a card drawn at random is a perfect square
$=\frac{\text { Number of favourable outcomes }}{\text { Total number of outcomes }}$
$=\frac{6}{48}=\frac{1}{8}$

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Question 31 Mark

A card is drawn at random from a well shuffled pack of $52$ playing cards. Find the probability of getting neither a red card nor a queen.

Answer

There are 26 red cards and $26$ black cards in a pack of $52$ playing cards.
Total number of outcome $=52$
Favorable number of outcome $($neither a red card nor a queen $)=52-(26+2)=24$
Probability of getting neither a red card nor a queen
$=\frac{\text { number of favourable outcomes }}{\text { total number of outcomes }}$
$=\frac{24}{52}=\frac{6}{13}$
Hence, the probability of getting neither a red card nor a queen is $\frac{6}{13}$.

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Question 41 Mark

What is the probability that a randomly taken leap year has 52 Sundays?

Answer

A leap year has 366 days $=52$ weeks and 2 days
Now, 52 weeks contain 52 Sundays
The remaining 2 days can be :
(i) Sunday and Mondays
(ii) Monday and Tuesday
(iii) Tuesday and Wednesday
(iv) Thursday and Friday
(v) Wednesday and Thursday
(vi) Friday and Saturday
(vii)Saturday and Sunday
Out of these 7 cases, there are 5 cases favouring it not to be Sunday.

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Question 51 Mark

If a number x is chosen at random from the numbers $-3,-2,-1,0,1,2,3$, then find the probability of $x^2<4$.

Answer

$
\begin{aligned}
x & =-3,-2,-1,0,1,2,3 \\
x^2 & =9,4,1,0,1,4,9
\end{aligned}
$
Total number of outcomes $=7$
Number of favourable outcomes $=3$
$
\begin{array}{c}
\left(x^2<4\right) \\
\therefore \quad P\left(x^2<4\right)=\frac{3}{7}
\end{array}
$

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Question 61 Mark

A dice is thrown once. What is the probability of getting a prime number.

Answer

Total number of outcomes $=6$
Number of favourable outcomes
$
\begin{aligned}
=2,3,5 =3 \\
P(E) =\frac{3}{6} \\
\Rightarrow P(E) =\frac{1}{2}
\end{aligned}
$

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Question 71 Mark

A coin is tossed twice. Find the probability of getting head both the times.

Answer

Possible outcomes = HH, HT, TH, TT
Total no. of outcomes $=4$
No. of favourable outcomes = 1 (both Heads)
$
P(E)=\frac{1}{4}
$

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