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JEE MATHEMATICS MCQ: PROBABILITY

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Let AA and BB be two events such that P(A)=0.3P(A)=0.3 and P(A∪B)=0.8P(A \cup B)=0.8. If AA and BB are independent events, then P(B)=P(B)=
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Correct option: A
5/75 / 7
Option A (5/75 / 7) is correct because it is the probability of event B calculated using the independence of events A and B, and the formula for the probability of the union of two events.

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Consider the probability distribution

X:12345P(X):k22kk2k5k2\begin{array}{cccccc}X: & 1 & 2 & 3 & 4 & 5 \\ P(X): & k^2 & 2 k & k & 2 k & 5 k^2\end{array}
The value of P(X>2)P(X>2) is
A bag contains (2  n+1)\left( {2\;n + 1} \right) coins. It is known that nn of these coins have a head on both sides, whereas the remaining n+1n + 1 coins are fair. A coin is picked up at random from the bag and tossed. If the probability that the toss results in a head is 31/42, then nn is equal to The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05 . What is the probability that out of 5 such bulbs none will fuse after 150 days of use If AA and BB are two independent events such that P(A∩B′)=325P\left( {A \cap B'} \right) = \frac{3}{{25}} and P(A′∩B)=825P\left( {A' \cap B} \right) = \frac{8}{{25}}, then P(A)P\left( A \right) is equal to In a game two players AA and BB take turns in throwing a pair of fair dice starting with player AA and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before BB throws a total of 7 and BB 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 player wins. The probability of AA winning the game is A box contains 5 brown and 4 white socks. A man takes out two socks. The probability that they are of the same colour is
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