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## Sagot :

**Answer:**

(a) [tex]P(Two\ Positive) = 0.2775[/tex]

(b) It is not too low

**Step-by-step explanation:**

**Given**

[tex]P(Single\ Positive) = 0.15[/tex]

[tex]n = 2[/tex]

**Solving (a):**

[tex]P(Two\ Positive)[/tex]

**First, calculate the probability of single negative**

[tex]P(Single\ Negative) =1 - P(Single\ Positive)[/tex]** --- complement rule**

[tex]P(Single\ Negative) =1 - 0.15[/tex]

[tex]P(Single\ Negative) =0.85[/tex]

**The probability that two combined tests are negative is:**

[tex]P(Two\ Negative) = P(Single\ Negative) *P(Single\ Negative)[/tex]

[tex]P(Two\ Negative) = 0.85 * 0.85[/tex]

[tex]P(Two\ Negative) = 0.7225[/tex]

**Using the complement rule, we have:**

[tex]P(Two\ Positive) = 1 - P(Two\ Negative)[/tex]

**So, we have:**

[tex]P(Two\ Positive) = 1 - 0.7225[/tex]

[tex]P(Two\ Positive) = 0.2775[/tex]

**Solving (b): Is (a) low enough?**

Generally, when a probability is less than or equal to 0.05; such probabilities are extremely not likely to occur

**By comparison:**

[tex]0.2775 > 0.05[/tex]

**Hence, it is not too low**