Statistics: Probability Rules: Addition and Multiplication

In a class, P(student plays a sport) = 0.45, P(student plays an instrument) = 0.30, and P(student does both) = 0.12. Find the probability that a randomly chosen student plays a sport or an instrument.

A spinner has 8 equal sections numbered 1 through 8. Find the probability of spinning an even number or a number greater than 6.

Two events A and B are mutually exclusive. P(A) = 0.28 and P(B) = 0.35. Find P(A or B).

A card is drawn from a standard 52-card deck. Find the probability that the card is a king or a heart.

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. One marble is chosen, replaced, and then a second marble is chosen. Find the probability that both marbles are red.

A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. One marble is chosen and not replaced, then a second marble is chosen. Find the probability that both marbles are red.

Events A and B are independent. P(A) = 0.60 and P(B) = 0.25. Find P(A and B).

A student is selected at random from a school. P(student is a senior) = 0.22. Among seniors, P(student has a parking permit) = 0.70. Find the probability that the selected student is a senior and has a parking permit.

In a survey, 40% of students like math, 50% like science, and 20% like both math and science. Find the probability that a randomly selected student likes neither math nor science.

A fair six-sided die is rolled twice. Find the probability of rolling a 6 on the first roll and an odd number on the second roll.

A two-way table shows 120 students by grade level and whether they ride the bus. There are 50 freshmen, 70 sophomores, 35 freshmen who ride the bus, and 30 sophomores who ride the bus. Find the probability that a randomly chosen student is a freshman or rides the bus.

For two events A and B, P(A) = 0.55, P(B) = 0.40, and P(A or B) = 0.75. Find P(A and B), then state whether A and B are mutually exclusive.