A group of researchers is investigating jungles of Kipling in search of Tabas. T
ID: 3329892 • Letter: A
Question
A group of researchers is investigating jungles of Kipling in search of Tabas. There is a 44% probability that they will actually see a Taba in the village among the giant kava trees. However, the probability that they will see a Joji during their expedition is fifty-four percent. 37% of the time the researchers will see neither a Taba nor a Joji. Construct a probability matrix (Punnitt Square) and use it to solve for the following probabilities.
a. If a researcher is selected at random, what is the probability that the researcher saw a Taba?
b. If a researcher is selected at random, what is the probability that the researcher saw a Joji?
c. If a researcher is selected at random, what is the probability that the researcher saw both a Taba and Joji?
d. If a researcher is selected at random, what is the probability that the researcher saw either a Taba or a Joji?
e. If a researcher is selected at random, what is the probability that the researcher saw neither a Taba nor a Joji?
f. If a researcher is selected at random, what is the probability that the researcher saw either Taba or a Joji, but not both?
g. If a researcher is selected at random, what is the probability that the researcher saw a Taba but not a Joji?
Explanation / Answer
a) P(researcher saw a Taba) = 0.44
b) P(researcher saw a Joji) = 0.54
c) P(researcher saw a Taba or Joji) = 1 - P(researchers will see neither a Taba nor a Joji) = 1 - 0.37 = 0.63
P( researcher saw both a Taba and Joji) = P(researcher saw a Taba) + P(researcher saw a Joji) - P(researcher saw a Taba or Joji)
= 0.44 + 0.54 - 0.63
= 0.35
d) P(researcher saw either a Taba or a Joji) = 0.63
e) P(researcher saw neither a Taba nor a Joji) = 0.37
f) P(researcher saw either Taba or a Joji, but not both) = P(researcher saw either a Taba or a Joji) - P( researcher saw both a Taba and Joji)
= 0.63 - 0.35
= 0.28
g) P(researcher saw a Taba but not a Joji) = P(researcher saw a Taba) - P( researcher saw both a Taba and Joji)
= 0.44 - 0.35
= 0.09
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