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A hat contains 12 cards marked with a star and 18 unmarked cards. What is the probability that one card slelected at random will be marked with a star?

A hat contains 12 cards marked with a star and 18 unmarked cards. What is the probability that one card slelected at random will be marked with a star? Correct Answer 2/5

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There are two boxes. Box I contains one white card and two black cards and Box II contains one white card and a black card. Two persons P and Q play a game. P picks a card randomly from Box I. If P finds the white card, P wins and the game stops. If P finds the black card, Q draws a card randomly from Box II. If Q finds the white card Q wins. The game stops whether Q draws the white card or P draws the white card. Which one of the following is correct?
The primitive translation vectors of the body centred cubic lattice are $$\overrightarrow {\bf{a}} = \frac{a}{2}\left( {{\bf{\hat x}} + {\bf{\hat y}} - {\bf{\hat z}}} \right),\,\overrightarrow {\bf{b}} = \frac{a}{2}\left( { - {\bf{\hat x}} + {\bf{\hat y}} + {\bf{\hat z}}} \right)$$        and $$\overrightarrow {\bf{c}} = \frac{a}{2}\left( {{\bf{\hat x}} - {\bf{\hat y}} + {\bf{\hat z}}} \right)$$    . The primitive translation vectors $$\overrightarrow {\bf{A}} ,\,\overrightarrow {\bf{B}} $$  and $$\overrightarrow {\bf{C}} $$ of the reciprocal lattice are
Smitha's collection of 113 greeting cards include a mix of birthday cards, new year cards, Diwali cards, Christmas cards, and a marriage anniversary card. The number of birthday cards is equal to the sum of all the others except the marriage anniversary card. The number of new year's cards is double the number of Diwali cards. Which in turn is double the number of Christmas cards. Then the ratio of the birthday cards to the Christmas cards in her collection is
Among the five stars, Star Z, Star Y, Star X, Star W, and Star V, Star W is brighter than Star Y and Star X. Star Z is dimmer than Star Y but brighter than Star X. Star V is brighter than Star Z but dimmer than Star Y. Which star is the second brightest?
A pack of the card contains some Black cards, Red cards and Blue cards such that the probability of picking a Black card is 2/7 and the probability of picking a Red card is 1/2. If all the cards are numbered starting from 1, 2, 3, …. and so on, then what is the probability of getting one card numbered as multiple of 3 or 7 out of the total cards.
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If the resultant of \(\vec{A}=6\hat{A}\) and \(\vec{B}=8\hat{B}\) is \(\vec{R}=10\hat{R}\) where \(\hat{A},\hat{B}\) and \(\hat{R}\) are the unit vectors along \(\vec{A},\vec{B}\) and \(\vec{R}\), then the value of \(\vec{A}\cdot \vec{B}\) will be
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