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Carleton University
Lisa R.
Intro Stats / AP Statistics
1 year, 1 month ago
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Probability Answer each of the following questions regarding probability: For the purposes of this worksheet assume the following A coin always lands on either heads or tails A deck of cards has 52 cards There are four suits (clubs; hearts; diamonds, and spades} each with 13 cards There are two colors (black and red) each with 26 cards Problems: 1. If | flip fair coin; what is the chance of the coin coming up heads? 2. If draw playing card from shuffled deck; what is the chance of the card being red? 3. If | flip two fair coins at the same time; what is the chance of the coins both comping up heads? 4. If draw two playing cards at the same time from shuffled deck; what is the chance of both cards being red? 5. Why are the answers to problems and 2 the same but the answers to problems 3 and 4 different?
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Abbey M.
asked • 07/12/191 Expert Answer
Gavin D. answered • 08/07/19 Experienced Tutor Specializing in a Variety of Math Subjects
The probability of drawing the initial 10 is 4 (the number of 10s in the deck) out of 52 (the number of cards in the deck). This can be reduced by 4 to make 1 out of 13. Drawing a two would then be 4 out of 51, since we didn't replace the card. Finally, drawing a Jack from the remainder of the deck has a probability of 4 out of 50, or 2 out of 25. We multiply these three probabilities to find the probability of these three events happening in succession. 1/13 x 4/51 x 2/25 = (4 x 2 x 1)/(13 x 51 x 25) = 8/16575. This fraction cannot be reduced, and the corresponding decimal (0.0004826...) would be rounded to 0.000483, or 4.83 x 10^-4.
Since there are four jacks in a deck of 52 cards and, likewise, four "fives", the odds of drawing either a jack or a "five" are 8/52 or two in thirteen. The probability of drawing a Jack is one in thirteen. The probability of drawing a "five" is one in thirteen.