(A) Total number of ways to select $2$ people from $13$ is given by $n(S) = {}_{13}C_2 = \frac{13 \times 12}{2 \times 1} = 78$. Let $A$ be the event t

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(A) Total number of ways to select $2$ people from $13$ is given by $n(S) = {}_{13}C_2 = \frac{13 \times 12}{2 \times 1} = 78$. Let $A$ be the event that at least one woman is selected. The number of ways to select at least one woman is: $n(A) = ({}_5C_1 \times {}_8C_1) + ({}_5C_2 \times {}_8C_0) = (5 \times 8) + (10 \times 1) = 40 + 10 = 50$. Therefore,the probability $P(A) = \frac{n(A)}{n(S)} = \frac{50}{78} = \frac{25}{39}$.

Class 11 Mathematics Probability Permutation and Combination based Probability

Medium

$A$ total of $13$ people,consisting of $5$ women and $8$ men,have applied for a job. If $2$ people are to be selected from these $13$ people,what is the probability that at least one woman is selected?

A
$25/39$
B
$14/39$
C
$5/13$
D
$10/13$

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Class 11

Mathematics Questions

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Probability

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Permutation and Combination based Probability

$A$ basket contains $3$ mangoes and $3$ apples. If two fruits are selected at random,what is the probability of getting one mango and one apple?

Easy

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$A$ bag contains $4$ red, $3$ white, and $5$ blue balls. Three balls are drawn at a time randomly from the bag. Match the items from List-$I$ with those of List-$II$.
List-$I$ List-$II$
$A$. Probability of getting $1$ red, $1$ white and $1$ blue ball $(i)$ $\frac{3}{44}$
$B$. Probability of getting $2$ white and $1$ blue ball $(ii)$ $\frac{21}{55}$
$C$. Probability of getting $2$ red and $1$ white ball $(iii)$ $\frac{38}{55}$
$D$. Probability that none of the balls is white $(iv)$ $\frac{3}{11}$
$(v)$ $\frac{9}{110}$

MediumTS EAMCET 2018

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If all the letters of the word $MISSISSIPPI$ are rearranged,what is the probability that all $S$ come together?

Medium

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If $m$ rupee coins and $n$ ten paise coins are placed in a line,then the probability that the extreme coins are ten paise coins is

Difficult

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$A$ bag contains $21$ toys numbered $1$ to $21$. $A$ toy is drawn and then another toy is drawn without replacement. The probability that both toys will show even numbers is

EasyAP EAMCET 2022

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List-$I$	List-$II$
$A$. Probability of getting $1$ red, $1$ white and $1$ blue ball	$(i)$ $\frac{3}{44}$
$B$. Probability of getting $2$ white and $1$ blue ball	$(ii)$ $\frac{21}{55}$
$C$. Probability of getting $2$ red and $1$ white ball	$(iii)$ $\frac{38}{55}$
$D$. Probability that none of the balls is white	$(iv)$ $\frac{3}{11}$
	$(v)$ $\frac{9}{110}$

$A$ total of $13$ people,consisting of $5$ women and $8$ men,have applied for a job. If $2$ people are to be selected from these $13$ people,what is the probability that at least one woman is selected?

Similar Questions

$A$ basket contains $3$ mangoes and $3$ apples. If two fruits are selected at random,what is the probability of getting one mango and one apple?

If all the letters of the word $MISSISSIPPI$ are rearranged,what is the probability that all $S$ come together?

If $m$ rupee coins and $n$ ten paise coins are placed in a line,then the probability that the extreme coins are ten paise coins is

$A$ bag contains $21$ toys numbered $1$ to $21$. $A$ toy is drawn and then another toy is drawn without replacement. The probability that both toys will show even numbers is

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