A state runs a lottery in which 6 numbers are randomly selected from 42, without
ID: 3149781 • Letter: A
Question
A state runs a lottery in which 6 numbers are randomly selected from 42, without replacement. A player chooses 6 numbers before the state's sample is selected. (a) What is the probability that the 6 numbers chosen by a player match all 6 numbers in the state's sample? (b) What is the probability that 5 of the 6 numbers chosen by a player appear in the state's sample? (c) What is the probability that 4 of the 6 numbers chosen by a player appear in the state's sample? (d) If a player enters one lottery each week, what is the expected number of weeks until a player matches all 6 numbers in the state's sample?
Explanation / Answer
a)The probability that the 6 numbers chosen by a player match all 6 numbers in the state's sample =1/42C6
=1.906*10-7
b)probability that 5 of the 6 numbers chosen by a player appear in the state's sample= (6*36)/42C6 =
=4.117*10-5
c)probability that 4 of the 6 numbers chosen by a player appear in the state's sample =(6C2 * 36C2 )/42C6 =
=1.801*10-3
d)expected number of weeks until a player matches all 6 numbers in the state's sample =
=1*1.906*10-7 +2*1.906*10-7*(1- 1.906*10-7 )+........inf = 1.906*10-7 *(1*(1- 1.906*10-7 )+2*(1- 1.906*10-7 )2 +....)
= 1.906*10-7 *(1- 1.906*10-7 )/(1.906*10-7 )2 =5146588 weeks
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