1
JEE Main 2022 (Online) 29th July Evening Shift
+4
-1

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is:

A
$$\frac{4}{9}$$
B
$$\frac{5}{18}$$
C
$$\frac{1}{6}$$
D
$$\frac{3}{10}$$
2
JEE Main 2022 (Online) 29th July Morning Shift
+4
-1

Let $$S=\{1,2,3, \ldots, 2022\}$$. Then the probability, that a randomly chosen number n from the set S such that $$\mathrm{HCF}\,(\mathrm{n}, 2022)=1$$, is :

A
$$\frac{128}{1011}$$
B
$$\frac{166}{1011}$$
C
$$\frac{127}{337}$$
D
$$\frac{112}{337}$$
3
JEE Main 2022 (Online) 28th July Evening Shift
+4
-1

Let $$\mathrm{A}$$ and $$\mathrm{B}$$ be two events such that $$P(B \mid A)=\frac{2}{5}, P(A \mid B)=\frac{1}{7}$$ and $$P(A \cap B)=\frac{1}{9} \cdot$$ Consider

(S1) $$P\left(A^{\prime} \cup B\right)=\frac{5}{6}$$,

(S2) $$P\left(A^{\prime} \cap B^{\prime}\right)=\frac{1}{18}$$

Then

A
Both (S1) and (S2) are true
B
Both (S1) and (S2) are false
C
Only (S1) is true
D
Only (S2) is true
4
JEE Main 2022 (Online) 28th July Morning Shift
+4
-1

Out of $$60 \%$$ female and $$40 \%$$ male candidates appearing in an exam, $$60 \%$$ candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. A candidate is randomly chosen from the qualified candidates. The probability, that the chosen candidate is a female, is :

A
$$\frac{2}{3}$$
B
$$\frac{11}{16}$$
C
$$\frac{23}{32}$$
D
$$\frac{13}{16}$$
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