1

### JEE Main 2019 (Online) 9th January Morning Slot

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P (X = 2) equals :
A
$25 \over 169$
B
$49\over 169$
C
$24 \over 169$
D
$52 \over 169$

## Explanation

P (X = 1) means out of two drawn cards one card is ace.

and P(X = 2) means both the drawn cards are ace.

$\therefore$  P(X = 1) = first card is ace or 2nd card is ace.

= A $-$ $+$ $-$ A

= ${4 \over {52}} \times {{48} \over {52}} + {{48} \over {52}} \times {4 \over {52}}$

= $2 \times {4 \over {52}} \times {{48} \over {52}}$

P(X = 2) =First and second both cards arc ace.

= A A

= ${4 \over {52}} \times {4 \over {52}}$

$\therefore$  P(X = 1) + P(X = 2)

= $2 \times {4 \over {52}} \times {{48} \over {52}} + {4 \over {52}} \times {4 \over {52}}$

= ${{25} \over {169}}$
2

### JEE Main 2019 (Online) 9th January Evening Slot

An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red, is :
A
${{21} \over {49}}$
B
${{27} \over {49}}$
C
${{26} \over {49}}$
D
${{32} \over {49}}$

## Explanation

5 Red and 2 green balls

P(one red ball) = ${5 \over 7}$

P(one green ball) = ${2 \over 7}$

Case I :

If drawn ball is green than a red ball is added

$\left( {\matrix{ {6{\mathop{\rm Re}\nolimits} d} \cr {1\,Green} \cr } } \right)$ P (red ball) = ${6 \over 7}$

Case II :

If drawn ball is red than a green ball is added

$\left( {\matrix{ {4{\mathop{\rm Re}\nolimits} d} \cr {3\,Green} \cr } } \right)$ P (red ball) = ${4 \over 7}$

P (2nd red ball) = ${5 \over 7}$ $\times {4 \over 7} + {2 \over 7} \times {6 \over 7}$ = ${{32} \over {49}}$
3

### JEE Main 2019 (Online) 10th January Morning Slot

An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered 1, 2, 3, ……, 9 is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is -
A
${{19} \over {36}}$
B
${{15} \over {72}}$
C
${{13} \over {36}}$
D
${{19} \over {72}}$

## Explanation

$P\left( A \right) = {1 \over 2} \times {{11} \over {36}} + {1 \over 2} \times {2 \over 9} = {{19} \over {72}}$
4

### JEE Main 2019 (Online) 10th January Evening Slot

If the probability of hitting a target by a shooter, in any shot, is ${1 \over 3}$, then the minimum number of independent shots at the target required by him so that the probability of hitting the target atleast once is greater than ${5 \over 6}$ is -
A
4
B
6
C
5
D
3

## Explanation

$1 - {}^n{C_0}{\left( {{1 \over 3}} \right)^0}{\left( {{2 \over 3}} \right)^n} > {5 \over 6}$

${1 \over 6} > {\left( {{2 \over 3}} \right)^n}\,\, \Rightarrow \,\,0.1666 > {\left( {{2 \over 3}} \right)^n}$

${n_{\min }} = 5$

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