Example 10

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 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Since there 52 cards n(S) = Total number of cards = 52 There are 13 diamond cards Let A be event that diamond card is withdrawn So, n(A) = 13 Probability of A = P(A) = ﷐𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑖𝑎𝑚𝑜𝑛𝑑 𝑐𝑎𝑟𝑑𝑠﷮𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠﷯ = ﷐n(A)﷮n(S)﷯ = ﷐13﷮52﷯ = ﷐𝟏﷮𝟒﷯ Example 10 One card is drawn from a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) = ﷐𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑎𝑐𝑒 𝑐𝑎𝑟𝑑𝑠﷮𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠﷯ = ﷐n(A)﷮n(S)﷯ = ﷐4﷮52﷯ = ﷐1﷮13﷯ Probability that card is not an ace = P(B’) = 1 – P(B) = 1 – ﷐1﷮13﷯ = ﷐13 − 1﷮13﷯ = ﷐𝟏𝟐﷮𝟏𝟑﷯ 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) = ﷐𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑙𝑎𝑐𝑘 𝑐𝑎𝑟𝑑𝑠﷮𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑐𝑎𝑟𝑑𝑠﷯ = ﷐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 the 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 − 1﷮4﷯ = ﷐𝟑﷮𝟒﷯ 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, C’ is event that card is not black Probability card is not a black = P(C’) = 1 – P(C) = 1 – ﷐1﷮2﷯ = ﷐𝟏﷮𝟐﷯