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17 Jun 2022, 01:30
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When an experiment is conducted 3 times, with the experiments being independent of one another, the probability that an event A occurs exactly 0, 1, or 2 times is \(\frac{98}{125}\). What is the probability that event A occurs when the experiment is conducted once?
A. \(\frac{1}{125}\)
B. \(\frac{27}{125}\)
C. \(\frac{1}{2}\)
D. \(\frac{14}{25}\)
E. \(\frac{3}{5}\)
Are You Up For the Challenge: 700 Level Questions
A. \(\frac{1}{125}\)
B. \(\frac{27}{125}\)
C. \(\frac{1}{2}\)
D. \(\frac{14}{25}\)
E. \(\frac{3}{5}\)
Are You Up For the Challenge: 700 Level Questions
17 Jun 2022, 02:34
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Event A occurs exactly 0, 1, 2, or 3 times is 1.
Event A occurs exactly 0, 1, or 2 times is 98/125
So the Event A occurs exactly three times is 27/125.
Let x be the probability that event A occurs when the experiment is conducted once.
x^3=27/125
=> x=3/5
The answer is thus (E).
Event A occurs exactly 0, 1, or 2 times is 98/125
So the Event A occurs exactly three times is 27/125.
Let x be the probability that event A occurs when the experiment is conducted once.
x^3=27/125
=> x=3/5
The answer is thus (E).
17 Jun 2022, 04:58
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Let the probability of event A happening once be P(X)
Also, since the probability that an event A occurs exactly 0, 1, or 2 times is 98/125,
The probability of event A occuring three times will be 1 - 98/125 = 27/125
Also, probability of event A happening 3 times = P(X)*P(X)*P(X) = 27/125
Thus, P(X) = 3/5
Thus, the correct option is E.
Also, since the probability that an event A occurs exactly 0, 1, or 2 times is 98/125,
The probability of event A occuring three times will be 1 - 98/125 = 27/125
Also, probability of event A happening 3 times = P(X)*P(X)*P(X) = 27/125
Thus, P(X) = 3/5
Thus, the correct option is E.
