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The probability of happening of an event...

The probability of happening of an event is 0.6 for one experiment. In three such experiments, find the probability of happening the event at least one time.

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To solve the problem, we need to find the probability of an event happening at least once in three experiments, given that the probability of the event occurring in a single experiment is 0.6. ### Step-by-Step Solution: 1. **Identify the Probability of the Event**: - Let \( P(E) \) be the probability of the event occurring in one experiment. - Given: \( P(E) = 0.6 \). **Hint**: Remember that probabilities range from 0 to 1, where 0 means the event will not happen and 1 means it will certainly happen. 2. **Calculate the Probability of the Event Not Occurring**: - The probability of the event not occurring (denoted as \( P(E') \)) is given by: \[ P(E') = 1 - P(E) = 1 - 0.6 = 0.4 \] **Hint**: The complement of an event is simply 1 minus the probability of the event. 3. **Determine the Probability of the Event Not Occurring in All Three Experiments**: - Since the experiments are independent, the probability that the event does not occur in all three experiments is: \[ P(E' \text{ in 3 experiments}) = P(E') \times P(E') \times P(E') = (P(E'))^3 = (0.4)^3 \] - Calculate \( (0.4)^3 \): \[ (0.4)^3 = 0.4 \times 0.4 \times 0.4 = 0.064 \] **Hint**: When dealing with independent events, multiply their probabilities together. 4. **Calculate the Probability of the Event Occurring at Least Once**: - The probability of the event occurring at least once in three experiments is given by: \[ P(\text{at least one } E) = 1 - P(E' \text{ in 3 experiments}) = 1 - 0.064 \] - Thus: \[ P(\text{at least one } E) = 1 - 0.064 = 0.936 \] **Hint**: The probability of at least one occurrence is the complement of the probability of no occurrences. ### Final Answer: The probability of the event occurring at least once in three experiments is \( 0.936 \).

To solve the problem, we need to find the probability of an event happening at least once in three experiments, given that the probability of the event occurring in a single experiment is 0.6. ### Step-by-Step Solution: 1. **Identify the Probability of the Event**: - Let \( P(E) \) be the probability of the event occurring in one experiment. - Given: \( P(E) = 0.6 \). ...
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NAGEEN PRAKASHAN ENGLISH-PROBABILITY-EXERCISE
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  14. In one toss of a coin, find the probability of getting: (i) head (ii...

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