1
COMEDK 2024 Evening Shift
+1
-0

A coin is tossed until a head appears or until the coin has been tossed three times. Given that 'head' does not appear on the first toss, what is the probability that the coin is tossed thrice?

A
$$\frac{1}{2}$$
B
$$\frac{3}{8}$$
C
$$\frac{1}{8}$$
D
$$\frac{1}{4}$$
2
COMEDK 2024 Evening Shift
+1
-0

Suppose we have three cards identical in form except that both sides of the first card are coloured red, both sides of the second are coloured black, and one side of the third card is coloured red and the other side is coloured black. The three cards are mixed and a card is picked randomly. If the upper side of the chosen card is coloured red, what is the probability that the other side is coloured black.

A
$$\frac{1}{6}$$
B
$$\frac{1}{2}$$
C
0
D
$$\frac{1}{3}$$
3
COMEDK 2024 Evening Shift
+1
-0

What is the probability of a randomly chosen 2 digit number being divisible by 3 ?

A
$$\frac{2}{9}$$
B
$$\frac{2}{3}$$
C
$$\frac{1}{3}$$
D
$$\frac{1}{9}$$
4
COMEDK 2024 Morning Shift
+1
-0

A and B each have a calculator which can generate a single digit random number from the set $$\{1,2,3,4,5,6,7,8\}$$. They can generate a random number on their calculator. Given that the sum of the two numbers is 12 , then the probability that the two numbers are equal is

A
$$\frac{5}{64}$$
B
$$\frac{1}{5}$$
C
$$\frac{1}{16}$$
D
$$\frac{1}{8}$$
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