Question 12 Marks
Two cards are selected from a pack of $52$ cards one by one without replacement. Find the probability of getting an ace and a king in that order.
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Find the probability that at least one die shows digit $4 ,$ when two dice are thrown simultaneously.
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There are $3$ yellow and $7$ white flowers in a basket. Two flowers are selected one by one without replacement from it. Find the probability that the first flower is yellow and the second flower is white.
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$7$ eitizens of country $A$ and $5$ citizens of country $B$ are traveling in an international flight of a company. After the routine security check, a higher level officer randomly selects $2$ citizens without replacement from the citizens of these two countries for additional security. Find the probability that both the selected citizens are from different countries.
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If $P(A)=\frac{2}{3}, P(B)=\frac{2}{5}$ and $P(A / B)=\frac{1}{2}$, find $P(B / A)$.
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The result of a school reveals that $20 \%, 15 \%$ and $30 \%$ students have failed in a school exam of standard $12$ in the subjects of Statistics, Economics and at least one of these subjects respectively. A student is selected at random from this school. If it is known that the student has failed in Economics, find probability that he has failed in Statistics, too.
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For a couple, the probability that the husband will be alive for next ten year is $0.7$ and that of his wife will be alive is $0.8$. The probability that both will be alive is $0.6$.
At the end of ten years. $(1)$ If the husband is alive, find the probability that the wife will be alive.
$(2)$ If the wife is alive, find the probability that the husband will be alive.
Answer$(1)\ \frac{6}{7}$ $(2)\ \frac{3}{4}$
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The probability of occurring at least one event out of two events $A$ and $B$ is $\frac{2}{3}$ and the probability of occuring $B$ but not $A$ is $\frac{1}{5}$. Find the probability of event $A$.
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Using the following information, find $P(A \cup B \cup C)$ for three events $A, B$ and $C$ of the sample space of a random experiment$\begin{aligned} &P(A)=0.63, P(B)=0.44, P(C)=0.27, P(A \cap B)=0.23, P(A \cap C)=0.16, P(B \cap C)=0.21, \\ &P(A \cap B \cap C)=0.04 \end{aligned} $
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A book of Statistics subject of $12 th$ standard is divided into two parts. There are $4$ chapters in part $1$ and $5$ chapters in part $2.$ A student selects any two chapters for revision in the end of January month.
$(1)$ Find the probability that the chapters selected by the student are from the same part.
$(2)$ Find the probability that the chapters selected by the student are from different parts
View full question & answer→Question 112 Marks
A teacher prepares schedule for the examination of seven subjects. Find the probability that the paper of Gujarati subject is scheduled immediately after the paper of English subject.
Answer$(1)\ \frac{4}{9}$
$(2)\ \frac{5}{15}$
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For two events $A$ and $B$ of sample space of a random experiment, $P(A)=0.7, P(B)=0.4$ and $P(A \cap B)=0.1$. Find $P(A-B)$ and $P\left(A^{\prime} \cap B^{\prime}\right)$.
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Two cards are selected at random from the pack of well-shuffled cards.
$(1)$ Find the probability of having both the cards of same suit.
$(2)$ Find the probability of having one face card
Answer$P(A-B)=0.6, P\left(A^{\prime} \cap B^{\prime}\right)=0$
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The sample space of a random experiment for selecting one number is $U=\{1,2,3, \ldots \ldots, 80\}$. All outcomes of this sample space are equiprobable.
$(1)$ Find the probability that the selected number is a multiple of $5.$
$(2)$ Find the probability that the selected number is not a multiple of $5.$
Answer$(1)\ \frac{4}{17}$
$(2)\ \frac{80}{221}$
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A number is selected from natural numbers $11$ to $100 .$ Find the probability that the selected number contains $9$ as one of the digits.
Answer$(1)\ \frac{1}{5}$
$(2)\ \frac{4}{5}$
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Find the probability of having both A together in all the arrangements of the letters of the word KATHAN.
Question 172 Marks
Find the probability of having $5$ Tuesdays in July month of a leap year.
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The weights $($in $kg )$ of $7$ students of a group are $52,58,70,65,50,56$ and $63$ respectively. One student is selected from this group, find the probability that his weight is greater than the average weight of the group.
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Three coins are tossed simultaneously. Find probability of getting more number of heads than the number of tails.
Question 202 Marks
Find the probability of getting at least one head when an unbiased coin is tossed three times.
Question 212 Marks
A die is thrown twice. Find the probability of having difference $2$ between the digits obtained on it.
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Write the rule of multiplication of probability of two events $A$ and $B$ of a sample space. Write the rule of multiplication of probability when two events $A$ and $B$ are independent.
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Write the rule of addition of probability for two events $A$ and $B$ of a sample space. If these events are mutually exclusive, write the rule of addition of probability.
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Explain equiprobable events with an illustration.
Question 252 Marks
Write the limitations of statistical definition of probability.
Question 262 Marks
Write the limitations of mathematical definition of probability.
Question 272 Marks
Write the assumptions of mathematical definition of probability.
Question 282 Marks
State the characteristics of a random experiment.