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Academy Algebra II/Trig

This worksheet covers theoretical and experimental probability, odds, compound events, and independent vs. dependent events. Practice problems include card drawing, dice rolling, and marble selection scenarios.

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Academy Algebra II/Trig

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  1. Academy Algebra II/Trig 14.3: Probability HW: worksheet Test: Thursday, 11/14

  2. Probability • Theoretical probability that event A will occur: • When an experiment is performed, the experimental probability of an event A is:

  3. Find the probability of selecting the following number from the numbers 1 – 50. 1.) a perfect square 2.) a factor of 150

  4. Odds • The odds that event A will occur:

  5. You randomly choose a marble from a bag of 10 black, 8 red, 4 white, and 6 blue. Find the indicated odds. 1.) in favor of choosing white 2.) against choosing red

  6. A card is randomly selected from a standard 52-card deck. Find the probability of drawing the given card. 1.) the king of diamonds 2.) a spade 3.) a red card

  7. The results of rolling a 6-sided die is shown. Find the experiment and theoretical probability. 1.) rolling an even # 2.) rolling a # less than 5

  8. Compound Events Or in probability means union. And in probability means intersection.

  9. Union of Events: overlapping vs. disjoint If they have nothing in common there will be nothing to subtract.

  10. A card is randomly drawn from a standard deck of 52 cards. Find the probability of drawing the indicated card. 1.) A heart or a diamond 2.) A spade or an even card

  11. A card is randomly drawn from a standard deck of 52 cards. Find the probability of drawing the indicated card. 3.) A 6 or a 7 4.) An ace or a spade

  12. A card is randomly drawn from a standard deck of 52 cards. Find the probability of drawing the indicated card. 5.) An ace and a spade 6.) A face card and a 4

  13. Probability of the Complement of an Event The event A, called the complement of event A, consists of all outcomes that are not in A. The probability of the complement of A is

  14. Independent vs. Dependent Events Independent events: 2 events are independent if the occurrences of one has no effect on the other. Dependent events: the occurrences of one affects the occurrence of the other. means the probability that B will occur given that A has occurred (conditional prob).

  15. A hat contains 10 blue,4 red,& 6 white marbles. 1.) Find the probability of choosing a red, then a white marble with replacement, then without replacement.

  16. A hat contains 10 blue,4 red,& 6 white marbles. 2.) Three marbles are chosen with replacement, find the probability that they are not white. Find the probability that at least one is white.

  17. Find the probability of drawing the given cards from a standard deck of 52 cards (a) with replacement and (b) without replacement. 1.) a heart, then a spade 2.) a king, then a queen

  18. Find the probability of drawing the given cards from a standard deck of 52 cards (a) with replacement and (b) without replacement. 3.) a 4, then a 3, then a 2 4.) a 10, then a 10, then another 10

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