A pair of fair dice is rolled. Let E denote the event that the number falling uppermost on the first die is 5, and let F denote the event that the sum of the numbers falling uppermost is 10. a. Compute P(F). b. Compute P(E ∩ F). c. Compute P(F | E). …

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A pair of fair dice is rolled. What is the probability that the sum of the numbers falling uppermost is less than 9, given that at least one of the numbers is a 6?

A pair of fair dice is rolled. What is the probability that the number landing uppermost on the first die is a 4 if it is known that the sum of the numbers landing uppermost is 7?

A pair of fair dice is rolled. Let E denote the event that the number landing uppermost on the first die is a 3, and let F denote the event that the sum of the numbers landing uppermost is 7. Determine whether E and F are independent events.

A card is drawn from a well-shuffled deck of 52 playing cards. Let E denote the event that the card drawn is black and let F denote the event that the card drawn is a spade. Determine whether E and F are independent events. Give an intuitive explanation for your answer.

PRODUCT RELIABILITY The probability that a battery will last 10 hr or more is .80, and the probability that it will last 15 hr or more is .15. Given that a battery has lasted 10 hr, find the probability that it will last 15 hr or more.

Two cards are drawn without replacement from a wellshuffled deck of 52 playing cards. a. What is the probability that the first card drawn is a heart? b. What is the probability that the second card drawn is a heart if the first card drawn was not a heart? c. What is the probability that …

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Five black balls and four white balls are placed in an urn. Two balls are then drawn in succession. What is the probability that the second ball drawn is a white ball if a. The second ball is drawn without replacing the first? b. The first ball is replaced before the second is drawn?

AUDITING TAX RETURNS A tax specialist has estimated that the probability that a tax return selected at random will be audited is .02. Furthermore, he estimates that the probability that an audited return will result in additional assessments being levied on the taxpayer is .60. What is the probability that a tax return selected at …

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STUDENT ENROLLMENT At a certain medical school, of the students are from a minority group. Of those students who belong to a minority group, are black. a. What is the probability that a student selected at random from this medical school is black? b. What is the probability that a student selected at random from …

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