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Two coins are tossed 1000 times and the ...

Two coins are tossed 1000 times and the outcomes are recorded as under :
`|{:("Number of heads"," 2 1 0"),("Frequency","266 540 194"):}|`
A coin is thrown at random. What is the probability of getting at most one head.

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To solve the problem, we need to find the probability of getting at most one head when two coins are tossed 1000 times. ### Step-by-Step Solution: 1. **Understand the Outcomes**: - When two coins are tossed, the possible outcomes for the number of heads can be: - 2 heads - 1 head - 0 heads 2. **Record the Frequencies**: - From the given data, we have: - Frequency of 2 heads = 266 - Frequency of 1 head = 540 - Frequency of 0 heads = 194 3. **Define "At Most One Head"**: - "At most one head" means we can have either 0 heads or 1 head. Therefore, we need to consider the frequencies for both of these outcomes. 4. **Calculate the Total Frequency for At Most One Head**: - Total frequency for at most one head = Frequency of 0 heads + Frequency of 1 head - Total frequency = 194 (for 0 heads) + 540 (for 1 head) = 734 5. **Calculate the Total Number of Tosses**: - The total number of tosses is given as 1000. 6. **Calculate the Probability**: - Probability of getting at most one head = (Total frequency for at most one head) / (Total number of tosses) - Probability = 734 / 1000 7. **Simplify the Probability**: - The fraction 734/1000 can be simplified if needed, but in decimal form, it is 0.734. ### Final Answer: The probability of getting at most one head when two coins are tossed is \( \frac{734}{1000} \) or 0.734. ---
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