1
JEE Main 2024 (Online) 31st January Evening Shift
+4
-1

A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is

A
$$\frac{1}{9}$$
B
$$\frac{2}{9}$$
C
$$\frac{1}{27}$$
D
$$\frac{2}{27}$$
2
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

Three rotten apples are accidently mixed with fifteen good apples. Assuming the random variable $$x$$ to be the number of rotten apples in a draw of two apples, the variance of $$x$$ is

A
$$\frac{57}{153}$$
B
$$\frac{40}{153}$$
C
$$\frac{37}{153}$$
D
$$\frac{47}{153}$$
3
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is

A
$$\frac{4}{25}$$
B
$$\frac{2}{3}$$
C
$$\frac{2}{25}$$
D
$$\frac{4}{75}$$
4
JEE Main 2024 (Online) 30th January Evening Shift
+4
-1

Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn from it. The probability of drawing the ball from the bag A, if the ball drawn is white, is

A
1/4
B
1/3
C
3/10
D
1/9
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