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Suatu percobaa lempar undi tiga mata uang logam sebanyak kali. Frekuensi harapan munculnya dua sisi gambar dan satu sisi angka adalah....
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Q. Suatu percobaa lempar undi tiga mata uang logam sebanyak kali. Frekuensi harapan munculnya dua sisi gambar dan satu sisi angka adalah....
- Determine Probability: First, we need to determine the probability of getting exactly two heads and one tail in a single flip of three coins. There are possible outcomes that satisfy this condition: , , and , where represents heads and represents tails.
- Calculate Probabilities: To calculate the probability of each of these outcomes, we consider that each coin flip is independent and has two possible outcomes. The probability of getting heads (H) is , and the probability of getting tails (T) is also .
- Find Total Probability: The probability of getting HHT, for example, is . The same calculation applies to HTH and THH, so the probability for each of these outcomes is also .
- Calculate Expected Frequency: Since there are three favorable outcomes (HHT, HTH, THH), we multiply the probability of one outcome by to get the total probability of getting two heads and one tail in a single flip of three coins. So, .
- Calculate Expected Frequency: Since there are three favorable outcomes (HHT, HTH, THH), we multiply the probability of one outcome by to get the total probability of getting two heads and one tail in a single flip of three coins. So, .Now, to find the expected frequency of this event occurring over flips, we multiply the total probability by the number of flips. The expected frequency is .
- Calculate Expected Frequency: Since there are three favorable outcomes (HHT, HTH, THH), we multiply the probability of one outcome by to get the total probability of getting two heads and one tail in a single flip of three coins. So, .Now, to find the expected frequency of this event occurring over flips, we multiply the total probability by the number of flips. The expected frequency is .Calculating the expected frequency: . This means that we expect the combination of two heads and one tail to occur times out of flips.
