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The probability that an event A happens in one trial of an experiment is 0.4. Three independent trials of the experiment are performed. The probability that the event A happens at least once is (1980)
- a)0.936
- b)0.784
- c)0.904
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
The probability that an event A happens in one trial of an experiment ...
p = 0.4, n = 3, P (X ≥ 1) = ? ⇒ q = 0.6
∴ P (X ≥ 1) = 1– P (X = 0)
= 1– 3C0(0.4)0 (0.6)3 = 1 – 0.216 = 0.784
∴ P (X ≥ 1) = 1– P (X = 0)
= 1– 3C0(0.4)0 (0.6)3 = 1 – 0.216 = 0.784
Most Upvoted Answer
The probability that an event A happens in one trial of an experiment ...
To find the probability that event A happens at least once in three independent trials, we can use the concept of complementary probability. The complementary probability of an event is the probability that the event does not occur.
Let's calculate the probability that event A does not happen in one trial. Since the probability of event A happening in one trial is 0.4, the probability of event A not happening in one trial is 1 - 0.4 = 0.6.
Now, we can calculate the probability that event A does not happen in all three trials. Since the trials are independent, the probability that event A does not happen in all three trials is (0.6)^3 = 0.216.
The complementary probability of event A not happening in all three trials is the probability that event A happens at least once in three trials. So, the probability that event A happens at least once is 1 - 0.216 = 0.784.
Therefore, the correct answer is option 'B', 0.784.
Let's calculate the probability that event A does not happen in one trial. Since the probability of event A happening in one trial is 0.4, the probability of event A not happening in one trial is 1 - 0.4 = 0.6.
Now, we can calculate the probability that event A does not happen in all three trials. Since the trials are independent, the probability that event A does not happen in all three trials is (0.6)^3 = 0.216.
The complementary probability of event A not happening in all three trials is the probability that event A happens at least once in three trials. So, the probability that event A happens at least once is 1 - 0.216 = 0.784.
Therefore, the correct answer is option 'B', 0.784.
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The probability that an event A happens in one trial of an experiment is 0.4. Three independent trials of the experiment are performed. The probability that the event A happens at least once is (1980)a)0.936b)0.784c)0.904d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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