Practice GAT Quantitative Reasoning questions with answers and explanations.
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The equally likely outcomes are HH, HT, TH, and TT.
Exactly one head occurs in HT and TH, giving 2/4 = 1/2.
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Matrix addition is performed entry by entry.
Each corresponding pair sums to 5.
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There are 36 equally likely ordered outcomes.
Six outcomes have sum 7, so the probability is 6/36 = 1/6.
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For [[a, b], [c, d]], determinant = ad - bc.
Thus, 2 × 4 - 3 × 1 = 5.
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An event and its complement have total probability 1.
Thus, P(not A) = 1 - 0.35 = 0.65.
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An identity matrix has 1s on the main diagonal and 0s elsewhere.
It leaves a compatible matrix unchanged under multiplication.
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For independent events, multiply their probabilities.
Thus, 1/2 × 1/3 = 1/6.
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A square matrix is invertible only when its determinant is nonzero.
A zero determinant means the matrix is singular.
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There are 2 favorable blue balls out of 5 total balls.
The probability is therefore 2/5.
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The probability is 4/10 × 3/9.
This simplifies to 12/90 = 2/15.
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Three distinct objects can be arranged in 3! ways.
Thus, 3! = 3 × 2 × 1 = 6.
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The number of arrangements of 5 distinct objects is 5!.
Thus, 5! = 120.
