7.7: Mutually Inclusive Events: Overlapping Events and Probabili

In a factory, 90% of the machines are operating properly, and 85% of the workers are present on a given day. What is the probability that a randomly selected machine is operating properly and a randomly selected worker is present on the same day?

A die is rolled twice. What is the probability that the first roll results in a 4 and the second roll results in an even number?

Two cards are drawn sequentially from a standard deck of 52 cards. What is the probability that the first card drawn is a red card and the second card drawn is a face card?

In a school, the probability of a student passing a math test is 0.80, and the probability of passing a science test is 0.75. What is the probability that a student passes both the math test and the science test?

A bag contains 6 red balls, 4 blue balls, and 10 green balls. If two balls are drawn randomly with replacement, what is the probability that the first ball is red and the second ball is green?

A box contains 5 red balls and 3 blue balls. Two balls are drawn sequentially without replacement. What is the probability that both balls drawn are red?

A deck of 52 cards is shuffled, and two cards are drawn sequentially without replacement. What is the probability that the first card is a queen and the second card is a king?

In a bag of 10 marbles, 4 are red, 3 are green, and 3 are blue. If two marbles are drawn sequentially without replacement, what is the probability that both marbles are green?

A box contains 12 pencils, 5 of which are broken. If two pencils are selected sequentially without replacement, what is the probability that the first pencil is broken and the second pencil is also broken?

A spinner has 10 equal sections numbered 1 to 10. What is the probability of spinning either a multiple of 3 or an even number?

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