1 Marks

Question 11 Mark

If $P ( A )=\frac{5}{11}, P ( B )=\frac{6}{11}$ and $P ( A \cap B )=\frac{4}{11}$ then find $P\left(\frac{A}{ B }\right)$.

Answer

$
\because \quad P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)}
$
Put the values $P\left(\frac{A}{ B }\right)=\frac{\frac{4}{\frac{11}{6}}}{\frac{6}{11}}=\frac{4}{6}=\frac{2}{3} \quad$ Ans.

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Question 21 Mark

If a dice is rolled 3 times then find the probability of getting odd number on dice each time.

Answer

Odd number $1,3,5$ are come on dice by 3 types.
Number of results when one dice are rolled
$
=\{1,2,3,4,5,6\}
$
So, Probability of getting odd number $=\frac{3}{6}=\frac{1}{2}$ hence probability of getting odd number on 3 dice
$
=\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}=\frac{1}{8} \quad \text { Ans. }
$

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Question 31 Mark

If a dice is rolled once, then find the probability o multiple of 2 .

Answer

$
\begin{array}{l}
S=\{1,2,3,4,5,6\} \\
E=\{2,4,6\}
\end{array}
$
then$
\quad P(E)=\frac{3}{6}=\frac{1}{2}
$

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Question 41 Mark

What is the other name of Bayes' theorem?

Answer

Bayes' theorem is also known as the formula for the probability of "causes".

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Question 51 Mark

Tell that, division of a sample space is one or more.

Answer

Division of sample space can be more than one.

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Question 61 Mark

If $P(A)=\frac{5}{7}$ and $P(B)=0$, then can we find the value of $P ( A \mid B )$ ? If yes, find the value.

Answer

We know that $\quad P ( A \mid B )=\frac{ P ( A \cap B )}{ P ( B )}$, if $P ( B ) \neq 0$
but $\quad P ( B )=0$
Hence we cannot find $P ( A \mid B )$.

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