To find the probability of getting at least one contract, we can use the principle of Inclusion-Exclusion. The formula for two events A and B is:

P(A or B) = P(A) + P(B) - P(A and B)

Where:
P(A or B) is the probability of getting at least one contract.
P(A) is the probability of getting the hardware contract.
P(B) is the probability of not getting the software contract.
P(A and B) is the probability of getting both contracts.

Given:
P(A) = 3/4
P(B) = 5/9 (since this is the probability of not getting the software contract, the probability of getting the software contract is 1 - 5/9 = 4/9)
P(A and B) = 0.3944444444444444

Now we can plug these values into the formula:

P(A or B) = P(A) + (1 - P(B)) - P(A and B)
P(A or B) = 3/4 + (1 - 5/9) - 0.3944444444444444

First, calculate 1 - P(B):

1 - 5/9 = 9/9 - 5/9 = 4/9

Now, plug this into the formula:

P(A or B) = 3/4 + 4/9 - 0.3944444444444444

To add the fractions, we need a common denominator. The least common multiple of 4 and 9 is 36. So we convert the fractions:

P(A) = 3/4 = 27/36
1 - P(B) = 4/9 = 16/36

Now we can add them:

P(A or B) = 27/36 + 16/36 - 0.3944444444444444
P(A or B) = 43/36 - 0.3944444444444444

Now we need to convert 0.3944444444444444 to a fraction with a denominator of 36 to subtract it from 43/36. Since the decimal is repeating, we can round it to a close fraction for simplicity. The closest fraction to 0.3944444444444444 with a denominator of 36 is 14/36 (since 0.3944444444444444 ≈ 14/36).

P(A or B) = 43/36 - 14/36
P(A or B) = (43 - 14)/36
P(A or B) = 29/36

So the probability of getting at least one contract is 29/36.
적어도 하나의 계약을 체결할 확률을 구하려면 포함-제외 원칙을 사용할 수 있습니다. 두 이벤트 A와 B의 공식은 다음과 같습니다:

P(A 또는 B) = P(A) + P(B) - P(A와 B)

여기서
P(A 또는 B)는 적어도 하나의 계약을 체결할 확률입니다.
P(A)는 하드웨어 계약을 체결할 확률입니다.
P(B)는 소프트웨어 계약을 체결하지 않을 확률입니다.
P(A와 B)는 두 계약 모두 체결할 확률입니다.

주어진:
P(A) = 3/4
P(B) = 5/9(소프트웨어 계약을 체결하지 않을 확률이기 때문에 소프트웨어 계약을 체결할 확률은 1 - 5/9 = 4/9)
P(A와 B) = 0.3944444444444444444444444

이제 이 값들을 공식에 대입할 수 있습니다:

P(A 또는 B) = P(A) + (1 - P(B)) - P(A와 B)
P(A 또는 B) = 3/4 + (1 - 5/9) - 0.394444444444444444444444444

먼저 1 - P(B)를 계산합니다:

1 - 5/9 = 9/9 - 5/9 = 4/9

이제 이 값을 공식에 대입합니다:

P(A 또는 B) = 3/4 + 4/9 - 0.394444444444444444444444444

분수를 더하려면 공통 분모가 필요합니다. 4와 9의 최소공배수는 36입니다. 따라서 분수를 변환합니다:

P(A) = 3/4 = 27/36
1 - P(B) = 4/9 = 16/36

이제 더할 수 있습니다:

P(A 또는 B) = 27/36 + 16/36 - 0.39444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444