QuestionDecember 26, 2025

A number 1-40 is chosen at random. Find each probability. Write your answer as a simplified fraction. 3. P(multiple of3vert greater than15) Typearesponse

A number 1-40 is chosen at random. Find each probability. Write your answer as a simplified fraction. 3. P(multiple of3vert greater than15) Typearesponse
A number 1-40 is chosen at
random. Find each probability.
Write your answer as a simplified
fraction.
3. P(multiple of3vert greater than15)
Typearesponse

Solution
4.2(308 votes)

Answer

\frac{8}{25} Explanation 1. Identify total cases (greater than 15) Numbers greater than 15: 16 to 40 → total 40 - 15 = 25 numbers. 2. Identify favorable cases (multiples of 3 greater than 15) Multiples of 3 ≤ 40: 3,6,9,12,15,18,21,24,27,30,33,36,39. Greater than 15: 18,21,24,27,30,33,36,39 → 8 numbers. 3. Compute conditional probability Use **P(A|B) = \frac{P(A \cap B)}{P(B)}** Here, P(A|B) = \frac{8}{25}.

Explanation

1. Identify total cases (greater than 15)<br /> Numbers greater than 15: $16$ to $40$ → total $40 - 15 = 25$ numbers.<br /><br />2. Identify favorable cases (multiples of 3 greater than 15)<br /> Multiples of 3 ≤ 40: $3,6,9,12,15,18,21,24,27,30,33,36,39$. <br /> Greater than 15: $18,21,24,27,30,33,36,39$ → $8$ numbers.<br /><br />3. Compute conditional probability<br /> Use **$P(A|B) = \frac{P(A \cap B)}{P(B)}$** <br />Here, $P(A|B) = \frac{8}{25}$.
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