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

Example 10 - Chapter 16 Class 11 Probability - Part 2
Example 10 - Chapter 16 Class 11 Probability - Part 3
Example 10 - Chapter 16 Class 11 Probability - Part 4
Example 10 - Chapter 16 Class 11 Probability - Part 5
Example 10 - Chapter 16 Class 11 Probability - Part 6
Example 10 - Chapter 16 Class 11 Probability - Part 7
Example 10 - Chapter 16 Class 11 Probability - Part 8


Transcript

Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that 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Since there 52 cards n(S) = Total number of cards = 52 There are 13 diamond cards Let A be event that diamond card is withdrawn So, n(A) = 13 Probability of A = P(A) = (π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘‘π‘–π‘Žπ‘šπ‘œπ‘›π‘‘ π‘π‘Žπ‘Ÿπ‘‘π‘ )/(π‘‡π‘œπ‘‘π‘Žπ‘™ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘Žπ‘Ÿπ‘‘π‘ ) = (n(A))/(n(S)) = 13/52 = 𝟏/πŸ’ Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that 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) = (π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘Žπ‘π‘’ π‘π‘Žπ‘Ÿπ‘‘π‘ )/(π‘‡π‘œπ‘‘π‘Žπ‘™ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘Žπ‘Ÿπ‘‘π‘ ) = (n(A))/(n(S)) = 4/52 = 1/13 Probability that card is not an ace = P(B’) = 1 – P(B) = 1 – 1/13 = (13 βˆ’ 1)/13 = 𝟏𝟐/πŸπŸ‘ Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that 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) = (π‘π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘™π‘Žπ‘π‘˜ π‘π‘Žπ‘Ÿπ‘‘π‘ )/(π‘‡π‘œπ‘‘π‘Žπ‘™ π‘›π‘’π‘šπ‘π‘’π‘Ÿ π‘œπ‘“ π‘π‘Žπ‘Ÿπ‘‘π‘ ) = (n(C))/(n(S)) = 26/52 = 𝟏/𝟐 Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be (iv) not a diamond From part (i) , A is the event that card is diamond So, A’ is event that card is not diamond Probability card is not a diamond = P(A’) = 1 – P(A) = 1 – 1/4 = (4 βˆ’ 1)/4 = πŸ‘/πŸ’ Example 10 One card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, calculate the probability that card will be (v) not a black card From part (iii) , C is the event that card is black So, C’ is event that card is not black Probability card is not a black = P(C’) = 1 – P(C) = 1 – 1/2 = 𝟏/𝟐

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.