1
JEE Main 2020 (Online) 4th September Evening Slot
+4
-1
In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws total a of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six. The game stops as soon as either of the players wins. The probability of A winning the game is :
A
$${5 \over {6}}$$
B
$${5 \over {31}}$$
C
$${31 \over {61}}$$
D
$${30 \over {61}}$$
2
JEE Main 2020 (Online) 3rd September Evening Slot
+4
-1
The probability that a randomly chosen 5-digit number is made from exactly two digits is :
A
$${{150} \over {{{10}^4}}}$$
B
$${{134} \over {{{10}^4}}}$$
C
$${{121} \over {{{10}^4}}}$$
D
$${{135} \over {{{10}^4}}}$$
3
JEE Main 2020 (Online) 3rd September Morning Slot
+4
-1
A dice is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of 4. Then the conditional probability that the score 4 has appeared atleast once is :
A
$${1 \over 8}$$
B
$${1 \over 9}$$
C
$${1 \over 4}$$
D
$${1 \over 3}$$
4
JEE Main 2020 (Online) 2nd September Evening Slot
+4
-1
Let EC denote the complement of an event E. Let E1 , E2 and E3 be any pairwise independent events with P(E1) > 0

and P(E1 $$\cap$$ E2 $$\cap$$ E3) = 0.

Then P($$E_2^C \cap E_3^C/{E_1}$$) is equal to :
A
$$P\left( {E_3^C} \right)$$ - P(E2)
B
$$P\left( {E_2^C} \right)$$ + P(E3)
C
$$P\left( {E_3^C} \right)$$ - $$P\left( {E_2^C} \right)$$
D
P(E3) - $$P\left( {E_2^C} \right)$$
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