Vanessa, a research director, is conducting an experiment to determine the effec
ID: 3046884 • Letter: V
Question
Vanessa, a research director, is conducting an experiment to determine the effectiveness of treatment for peach trees against blight. She randomly divides one grove's trees into three groups. One group is the control with no treatment for blight. She prunes the second group to remove the limbs showing blight after the spring rains. She prunes the third group as well and als sprays them with an antibiotic. Vanessa monitors the trees for five years after the start of the experiment. The table shows the outcomes, or the counts of how long the trees in each group lived. Treatment uning Antibiotic Totals 27 42 NonePr Outcomes 0 to 2 years 2 to 4 years More than 4 years Totals 102 114 35 40 28 15 83 101 120 304 Click to download the data in your preferred format if you wish. CrunchIt! CSV Excel JMP Mac Text Minitab PC Text R SPSS TI Calc Determine the probability that a randomly selected tree from this experiment lived two to four years or was treated with an antibiotic. Give your answer as a decimal, precise to three decimal places. probability:Explanation / Answer
We have to find P(2 to 4 years OR Antibiotic) = ?
P( A OR B) = P( A ) + P( B) - P( A AND B)
From given data table,
P( 2 to 4 years) = 114 / 304
P( Antibiotic) = 120 / 304
P( 2 to 4 years AND Antibiotic) = 42 / 304
Therefore
P(2 to 4 years OR Antibiotic) = P( 2 to 4 years) + P( Antibiotic) - P(2 to 4 years AND Antibiotic)
= 114 / 304 + 120 / 304 - 42 / 304
= 192 / 304
= 0.632 (Rounded to three decimal places)
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