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Chapter 13 Class 12 Probability

Ex 13.3, 12 - A card from a pack of 52 cards is lost - Ex 13.3

Ex 13.3, 12 - Chapter 13 Class 12 Probability - Part 2
Ex 13.3, 12 - Chapter 13 Class 12 Probability - Part 3 Ex 13.3, 12 - Chapter 13 Class 12 Probability - Part 4

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Transcript

Ex 13.3, 12 A card from a pack of 52 cards is lost. From the remaining cards of the pack, two cards are drawn and are found to be both diamonds. Find the probability of the lost card being a diamond.Let, E1 : Event that lost card is diamond E2 : Event that lost card is not a diamond A : Event that two cards drawn are diamond We need to find out that probability that the lost card being a diamond if two cards drawn are found to be both diamond. i.e. P(E1|A) P(E1|A) = (𝑃(𝐸_1 ).𝑃(𝐴|𝐸_1))/(𝑃(𝐸_1 ).𝑃(𝐴|𝐸_1)+𝑃(𝐸_2 ).𝑃(𝐴|𝐸_2) ) "P(E1)" = Probability that lost card is diamond = 13/52 = 𝟏/πŸ’ P(A|E1) = Probability of getting 2 diamond cards if lost card is diamond = β–ˆ(𝑆𝑒𝑙𝑒𝑐𝑑𝑖𝑛𝑔 2 π‘‘π‘–π‘Žπ‘šπ‘œπ‘›π‘‘ π‘π‘Žπ‘Ÿπ‘‘π‘  π‘“π‘Ÿπ‘œπ‘š @(13βˆ’1= 12)π‘‘π‘–π‘Žπ‘šπ‘œπ‘›π‘‘ π‘π‘Žπ‘Ÿπ‘‘π‘ )/(𝑆𝑒𝑙𝑒𝑐𝑑𝑖𝑛𝑔 π‘Žπ‘›π‘¦ 2 π‘π‘Žπ‘Ÿπ‘‘π‘  π‘“π‘Ÿπ‘œπ‘š 51 π‘π‘Žπ‘Ÿπ‘‘π‘ ) = 𝟏𝟐π‘ͺ𝟐/πŸ“πŸπ‘ͺ𝟐 = ((12 Γ— 11)/2!)/((51 Γ— 50)/2!) = (12 Γ— 11)/(51 Γ— 50) "P(E2)" = Probability that lost card is not a diamond = 1 – P(E1) = 1 – 1/4 = πŸ‘/πŸ’ P(A|E2) = Probability of getting 2 diamond cards if lost card is not a diamond = β–ˆ(𝑆𝑒𝑙𝑒𝑐𝑑𝑖𝑛𝑔 2 π‘‘π‘–π‘Žπ‘šπ‘œπ‘›π‘‘ π‘π‘Žπ‘Ÿπ‘‘π‘  @π‘“π‘Ÿπ‘œπ‘š 13 π‘‘π‘–π‘Žπ‘šπ‘œπ‘›π‘‘ π‘π‘Žπ‘Ÿπ‘‘π‘ )/(𝑆𝑒𝑙𝑒𝑐𝑑𝑖𝑛𝑔 π‘Žπ‘›π‘¦ 2 π‘π‘Žπ‘Ÿπ‘‘π‘  π‘“π‘Ÿπ‘œπ‘š 51 π‘π‘Žπ‘Ÿπ‘‘π‘ ) = πŸπŸ‘π‘ͺ𝟐/πŸ“πŸπ‘ͺ𝟐 = ((13 Γ— 12)/2!)/((51 Γ— 50)/2!) = (13 Γ— 12)/(51 Γ— 50) Putting value in the formula, P(E1|A) = (𝑃(𝐸_1 ).𝑃(𝐴|𝐸_1))/(𝑃(𝐸_1 ).𝑃(𝐴|𝐸_1)+𝑃(𝐸_2 ).𝑃(𝐴|𝐸_2) ) = (1/4 Γ— (12 Γ— 11)/(51 Γ— 50))/( 1/4 Γ— (12 Γ— 11)/(51 Γ— 50) + 3/4 Γ— (13 Γ— 12)/(51 Γ— 50) ) = (1/4 Γ— (12 )/(51 Γ— 50) (11))/( 1/4 Γ— 12/(51 Γ— 50) (11+ 3 Γ— 13) ) = 11/(11 + 39) = 𝟏𝟏/πŸ“πŸŽ Therefore, required probability is 11/50

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.