Two cards are drawn without replacement from a standard, well shuttled deck. Cal
ID: 3264480 • Letter: T
Question
Two cards are drawn without replacement from a standard, well shuttled deck. Calculate the probabilities for the following events. a) The first card is a Queen and the second is a spade _____ (round to 4 decimals) b) A pair (two of a kind) is drawn _______ Assume that girls and boys are equally likely and the event "having a girl" does not affect the future/past probability of "having a boy" and vice versa. Also, there are no twins. You see a woman walking on the street with a girl. She tells you that she has three children and that the girl with her is her daughter. a) What is the probability that she has two boys? ______ (enter a fraction) b) What is the probability that she has at least one boy? ______ (enter a fraction)Explanation / Answer
3)a ) probability =first card is non spade queen*second one spade+first card is queen of spade*second card is of spade
=(3/52)*(13/51)+(1/52)*(12/51)=0.0192
b)probabilty =first card is of any rank(*second card is of same rank =(52/52)*(12/51)=0.2353
4)a)there are 8 outcomes of 3 children =GGG, GGB,GBG,GBB,BBB,BBG,BGB,BGG
probability that she has at least one girl child =7/8 (there are 7 events out of 8 to have at least one girl)
therefore probabilty of having two boys; given one is girl =(3/8)/(7/8)=3/7 =0.4286
b) probability that alt least one boy given one is girl =(6/8)/(7/8)=6/7=0.8571
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