# Recent questions tagged conditional-probability

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A box contains $15$ blue balls and $45$ black balls. If $2$ balls are selected randomly, without replacement, the probability of an outcome in which the first selected is a blue ball and the second selected is a black ball, is _____ $\frac{3}{16}$ $\frac{45}{236}$ $\frac{1}{4}$ $\frac{3}{4}$
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An automobile plant contracted to buy shock absorbers from two suppliers $X$ and $Y.$ $X$ supplies $60\%$ and $Y$ supplies $40\%$ of the shock absorbers. All shock absorbers are subjected to a quality test. The ones that pass the quality test are considered reliable. Of $X'$s shock ... randomly chosen shock absorber, which is found to be reliable, is made by $Y$ is $0.288$ $0.334$ $0.667$ $0.720$
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If $P(X) = \displaystyle{\frac{1}{4}}$, $P(Y) = \displaystyle{\frac{1}{3}}$, and $P(X \cap Y) = \displaystyle{\frac{1}{12}}$, the value of $P(Y/X)$ is $\displaystyle{\frac{1}{4}} \\$ $\displaystyle{\frac{4}{25}} \\$ $\displaystyle{\frac{1}{3}} \\$ $\displaystyle{\frac{29}{50}}$
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You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is $1/4$ $1/3$ $1/2$ $2/3$
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The probability that a student knows the correct answer to a multiple choice question is $\dfrac{2}{3}$ . If the student does not know the answer, then the student guesses the answer. The probability of the guessed answer being correct is $\dfrac{1}{4}$. Given that the student has answered the question ... the correct answer is $\dfrac{2}{3} \\$ $\dfrac{3}{4} \\$ $\dfrac{5}{6} \\$ $\dfrac{8}{9}$
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