A card is being drawn from a standard deck of playing cards. Find each probability.
1 answer:
These are 6 questions and 6 answers. To find each probability we will use the definition of probability:Probability = number of positive outcomes / number of total possible outcomes 1) <span>P(Jack or ten) </span> <span>Answer: 2/13 ≈ 0.12 </span>Justification: i) Positive outcomes: A standard deck of cards has 4 jacks and 4 tens , then those are 4 + 4 = 8 different positive outcomes . ii) Possible outcomes: a standard deck of cards has 52 different cards , so, that is a total of 52 different possible outcomes iii) Probability, P P = number of positive outcomes / number of total possible outcomesP = 8 / 52 = 2/13 ≈ 0.15 <span>
2.P(red or black) </span>Answer: 1 Justification: i) Positive outcomes Half of the cards are red and half of the cards are black, so they both add for the total of the cards = 52 ii) Possible outcomes: 52 cards iii) Probaility, P P = number of positive outcomes / number of total possible outcomesP = 52 / 52 = 1 <span>
3.P(queen or club) </span>Answer: 4/13 ≈ 0.31 Justification: i) Positive outcomes There are 4 Queens. There are 1/4 of 52 clubs = 1/4 × 52 = 13 clubs. But you cannot add all of them, because one club is the Quenn of Clubs. Then, the total number of different Queens and clubs is 4 + 13 - 1 = 16 ii) Possible outcomes: 52 different cards iii) Probaility, P P = number of positive outcomes / number of total possible outcomes P = 16 /52 = 4 / 13 ≈ 0.31 <span>
4.P(red or ace) </span>Answer: 7 / 13 ≈ 0.54 Justification: i) Positive outcomes Half of the cards are red: 26 There are 4 aces. Since 2 aces are red, the number of different red and aces cards is: 26 + 4 - 2 = 28 ii) Possible outcomes: 52 different outcomes iii) Probaility, P P = number of positive outcomes / number of total possible outcomes P = 28 / 52 = 7 / 13 ≈ 0.54 <span>
5.P(diamond or black) </span><span>
</span>Answer: 1/2 = 0.5 Justification: i) Positive outcomes There are 52 / 4 = 13 diamonds There are 26 black cards. All the diamonds are black cards. Then, the number of different diamond or black cards is 13 + 26 - 13 = 26 ii) Possible outcomes: 52 different cards. iii) Probaility, P P = number of positive outcomes / number of total possible outcomesP = 26 / 52 = 1/2 = 0.5 6.P(face card or spade)
Answer: 11/26 ≈ 0.42 Justification: i) Positive outcomes Face cards are jacks, queens and kings. That is 3 × 4 = 12 different cards. The spades are 13 cards. Since, 3 of the faces are spade cards, the number of different cards of those types are 12 + 13 - 3 = 22 ii) Possible outcomes: 52 different cards iii) Probaility, P P = number of positive outcomes / number of total possible outcomesP = 22 / 52 = 11 / 26 ≈ 0.42
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