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Example 10 - One card is drawn from a well shuffled deck - Basic Formula

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  1. Chapter 16 Class 11 Probability
  2. Serial order wise
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Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be a diamond Since there 52 cards n(S) = Total number of cards = 52 There are 13 diamond cards Let A be event that diamond card is withdrawn So, n(A) = 13 Probability of A = P(A) = ๏ท๐‘๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘‘๐‘–๐‘Ž๐‘š๐‘œ๐‘›๐‘‘ ๐‘๐‘Ž๐‘Ÿ๐‘‘๐‘ ๏ทฎ๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™ ๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘๐‘Ž๐‘Ÿ๐‘‘๐‘ ๏ทฏ = ๏ทn(A)๏ทฎn(S)๏ทฏ = ๏ท13๏ทฎ52๏ทฏ = ๏ท๐Ÿ๏ทฎ๐Ÿ’๏ทฏ Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be (ii) not an ace There are 4 ace cards Let B be the event that card drawn is ace So, n(B) = 4 Hence Probability card drawn is ace = P(B) = ๏ท๐‘๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘Ž๐‘๐‘’ ๐‘๐‘Ž๐‘Ÿ๐‘‘๐‘ ๏ทฎ๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™ ๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘๐‘Ž๐‘Ÿ๐‘‘๐‘ ๏ทฏ = ๏ทn(A)๏ทฎn(S)๏ทฏ = ๏ท4๏ทฎ52๏ทฏ = ๏ท1๏ทฎ13๏ทฏ Probability that card is not an ace = P(Bโ€™) = 1 โ€“ P(B) = 1 โ€“ ๏ท1๏ทฎ13๏ทฏ = ๏ท13 โˆ’ 1๏ทฎ13๏ทฏ = ๏ท๐Ÿ๐Ÿ๏ทฎ๐Ÿ๐Ÿ‘๏ทฏ Example, 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be (iii) a black card (i.e., a club or, a spade) There are 26 black cards (13 spade and 13 club) Let C be the probability that card drawn is black n(C) = 13 + 13 = 26 Hence Probability card drawn is black = P(C) = ๏ท๐‘๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘๐‘™๐‘Ž๐‘๐‘˜ ๐‘๐‘Ž๐‘Ÿ๐‘‘๐‘ ๏ทฎ๐‘‡๐‘œ๐‘ก๐‘Ž๐‘™ ๐‘›๐‘ข๐‘š๐‘๐‘’๐‘Ÿ ๐‘œ๐‘“ ๐‘๐‘Ž๐‘Ÿ๐‘‘๐‘ ๏ทฏ = ๏ทn(C)๏ทฎn(S)๏ทฏ = ๏ท26๏ทฎ52๏ทฏ = ๏ท๐Ÿ๏ทฎ๐Ÿ๏ทฏ Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be (iv) not a diamond From part (i) , A is the event that card is diamond So, Aโ€™ is event that card is not diamond Probability card is not a diamond = P(Aโ€™) = 1 โ€“ P(A) = 1 โ€“ ๏ท1๏ทฎ4๏ทฏ = ๏ท4 โˆ’ 1๏ทฎ4๏ทฏ = ๏ท๐Ÿ‘๏ทฎ๐Ÿ’๏ทฏ Example, 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that the card will be (v) not a black card From part (iii) , C is the event that card is black So, Cโ€™ is event that card is not black Probability card is not a black = P(Cโ€™) = 1 โ€“ P(C) = 1 โ€“ ๏ท1๏ทฎ2๏ทฏ = ๏ท๐Ÿ๏ทฎ๐Ÿ๏ทฏ

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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