Ex 16.3, 4

Transcript

Ex 16.3, 4 A card is selected from a pack of 52 cards. • How many points are there in the sample space? Since these are 52 cards these are 52 points in this sample space n(S) = 52 Ex 16.3, 4 (b) Calculate the probability that the card is an ace of spades. Here, n(s) = 52 There are 13 spade cards out of which only 1 is ace Let A be the event of ace spade card selected n(A) = 1 Probability that ace spade card is selected = P(A) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑐𝑒 𝑠𝑝𝑎𝑑𝑒 𝑐𝑎𝑟𝑑﷮𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠﷯ = n(A)﷮n(S)﷯ = 𝟏﷮𝟓𝟐﷯ Ex16.3, 4 (c) Calculate the probability that the card is (i) an ace (ii) black card. (i) An ace There are 4 ace cards Let B be the event of getting an ace card n(B) = 4 Probability that ace card is selected from 52 cards = P(B) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑐𝑒 𝑐𝑎𝑟𝑑𝑠﷮𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠﷯ = n(B)﷮n(S)﷯ = 4﷮52﷯ = 𝟏﷮𝟏𝟑﷯ (ii) black card There are 26 black card in a pack of 52 cards Let C be the event of selecting a black card n(C) = 26 Hence P(C) = 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑙𝑎𝑐𝑘 𝑐𝑎𝑟𝑑𝑠﷮𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠﷯ = n(C)﷮n(S)﷯ = 26﷮52﷯ = 𝟏﷮𝟐﷯