Mathematics, Part 13
Question 1: Explain how to determine the probability that an event will not occur. Use the principle to determine the probability that a coin tossed four times will be heads at least once.
Answer 1: The probability that an event will occur and the probability that it will not occur are complementary. This means that their respective probabilities will sum to 1. Therefore, the probability that an event will not occur can be determined by first calculating the probability that it will occur and then subtracting that number from 1. To solve the problem, first take note that the only way the condition is not met is if the coin is tails all four times. The probability of that happening is (1/2)4 = 1/16. Take the complement of this probability by subtracting it from 1. 1 – 1/16 = 15/16Thus, the probability that a coin which is tossed four times will be heads at least once is 15/16.
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Question 2: One card is drawn at random from a standard deck of 52 cards. Determine the probability that the card will be:a diamondan acea face card (king, queen, or jack)
Answer 2: The probability of a desired occurrence can be found by dividing the number of desired outcomes by the total number of possible outcomes. The number of possible outcomes of the event of drawing one card from a deck of 52 cards is 52. Thirteen of the cards in the deck are diamonds. Therefore, the probability of drawing a diamond is 13/52 = 1/4.Four of the cards in the deck are aces. Therefore, the probability of drawing an ace is 4/52 = 1/13.Twelve of the cards in the deck are face cards (4 kings, 4 queens, and 4 jacks). Therefore, the probability of drawing a face card is 12/52 = 3/13.
Question 3: Suppose that angles CBE and BEF are interior one-sided angles and lines CB and EF are parallel. If the degree measure of CBE is twice as large as the degree measure of BEF, determine the degree measure of CBE?
Answer 3: Suppose that the degree measure of the angle BEF is x. The degree measure of the angle CBE must then be 2x. Since angles BEF and CBE are interior one-sided angles and lines CB and EF are parallel, the sum of their degree measures is 180. Therefore, using the formula x + 2x = 180 degrees, we determine that x = 60 degrees. Thus, angle CBE measures 120 degrees.
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