A customs agent discovers 24 identically looking packets of white power in a traveler's suitcase. Unknown to the customs officer, 18 of these packets contain cocaine, the rest do not contain cocaine. The customs officer is to randomly pick 4 packets and test each one. A random variable X is to count the number of tested packets that test positive for cocaine. (a) Finish the probability distribution of X below. Use four decimals in each of your entries. X P(X= x) 0 1 234 (b) From the distribution you found in part (a), what can you say about the distribution of X? The distribution of X is ? E(X)= (c) How many of the 4 packets do you expect be to test positive for cocaine? Provide the standard deviation as well. SD(X) = (use two decimals) V (use two decimals)
A customs agent discovers 24 identically looking packets of white power in a traveler's suitcase. Unknown to the customs officer, 18 of these packets contain cocaine, the rest do not contain cocaine. The customs officer is to randomly pick 4 packets and test each one. A random variable X is to count the number of tested packets that test positive for cocaine. (a) Finish the probability distribution of X below. Use four decimals in each of your entries. X P(X= x) 0 1 234 (b) From the distribution you found in part (a), what can you say about the distribution of X? The distribution of X is ? E(X)= (c) How many of the 4 packets do you expect be to test positive for cocaine? Provide the standard deviation as well. SD(X) = (use two decimals) V (use two decimals)
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 4ECP: Show that the probability of drawing a club at random from a standard deck of 52 playing cards is...
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Transcribed Image Text:A customs agent discovers 24 identically looking packets of white power in a traveler's suitcase. Unknown to the customs officer, 18 of these
packets contain cocaine, the rest do not contain cocaine.
The customs officer is to randomly pick 4 packets and test each one. A random variable X is to count the number of tested packets that test
positive for cocaine.
(a) Finish the probability distribution of X below. Use four decimals in each of your entries.
P(X = x)
0
1
(b) From the distribution you found in part (a), what can you say about the distribution of X?
E(X)
2 3 4
The distribution of X is ?
SD(X)
(c) How many of the 4 packets do you expect be to test positive for cocaine? Provide the standard deviation as well.
(use two decimals)
(use two decimals)
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