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6 problems match “dependent events”. Clear

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1. Die roll greater than two ●○○○○ 10 ptsA fair six-sided die is rolled three times. The results are 1, 4, and 3, in that order. What is the probability that the next roll will produce a number greater than 2? Round to two decimal places.
2. Ace then king without replacement ●○○○○ 10 ptsA standard 52-card deck is shuffled. One card is drawn and not replaced, then a second card is drawn. Find the probability that the first card is an ace and the second card is a king. Give your answer as a decimal rounded to four decimal places.
3. Equal heads from two coins ●●○○○ 20 ptsCoin $A$ is flipped three times and coin $B$ is flipped four times. Both coins are fair. What is the probability that the number of heads obtained from coin $A$ equals the number of heads obtained from coin $B$? Give your answer as a decimal.
4. Same number of heads for two flips ●●○○○ 20 ptsJackie and Phil have two fair coins and a third coin that comes up heads with probability $\frac{4}{7}$. Jackie flips the three coins, and then Phil flips the three coins. Let $\frac{m}{n}$ be the probability that Jackie gets the same number of heads as Phil, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
5. Second and third rolls exceed first ●●○○○ 20 ptsA fair six-sided die is rolled three times. Find the probability that the second and third rolls are both larger than the first roll. Round to two decimal places.
6. Matching head counts with unfair coin ●●●○○ 50 ptsJackie and Phil have two fair coins and a third coin that comes up heads with probability $\frac{4}{7}$. Jackie flips the three coins, and then Phil flips the three coins. Let $\frac{m}{n}$ be the probability that Jackie gets the same number of heads as Phil, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.