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56 problems match “probability”. Clear

Diastolic pressure below 70 ●○○○○ 10 ptsDiastolic blood pressures for men aged 35 to 44 are normally distributed with mean 80 mm Hg and standard deviation 10 mm Hg. What is the probability that a randomly chosen man in this age group has a diastolic blood pressure less than 70 mm Hg? Round to two decimal places.
Ace of spades before face cards ●●○○○ 20 ptsCarson flips over the cards of a standard 52-card deck one at a time. Find the probability that he flips over the ace of spades before any face card (jack, queen or king). Round to two decimal places.
Aces before the joker ●●○○○ 20 ptsA standard 52-card deck plus one joker (53 cards in total) is shuffled into a uniformly random order and turned over one card at a time. What is the probability that all 4 aces are turned over before the joker? Give your answer as a decimal.
Probability the game never stops ●●○○○ 20 ptsA box starts with one red ball and one blue ball. At each step, a ball is taken at random from the box. If it is red, the game stops. If it is blue, it is returned to the box together with one additional blue ball. Thus, at the $n$ -th draw the box contains $n+1$ balls, one of which is red. Find the probability that the game never stops.
Odd reciprocals with terminating decimals ●●○○○ 20 ptsIf $\frac{a}{b}$ is the probability that the reciprocal of a randomly selected positive odd integer less than $2010$ gives a terminating decimal, with $a$ and $b$ relatively prime positive integers, find $a+b$ .
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.
Removing an element to raise probability ●●○○○ 20 ptsTwo different numbers are randomly selected from the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11\}$ . The probability that their sum is 12 would be greater if the number $n$ had first been removed from $S$ . What is the value of $n$ ?
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 $m+n$ .
Win probability of die A against die B ●●○○○ 20 ptsDie A has faces $3, 3, 3, 3, 3, 6$ and die B has faces $2, 2, 2, 5, 5, 5$ , each face equally likely. Both dice are rolled at the same time. Find the probability that die A shows a higher value than die B. Round to two decimal places.
Win probability of die C against A ●●○○○ 20 ptsDie C has faces 1, 4, 4, 4, 4, 4 and die A has faces 3, 3, 3, 3, 3, 6, each face equally likely. Both dice are rolled at the same time. Find the probability that die C shows a higher value than die A. Round to two decimal places.