Question

10 fill in the blank 8 points a coin is tossed and a die with numbers 1-6 is rolled. what is p(heads and 3)? write answers as fractions in simplest form. type your answer...

Explanation:

Step1: Find P(heads)

A coin has 2 outcomes (heads, tails). So \( P(\text{heads})=\frac{1}{2} \).

Step2: Find P(3 on die)

A die has 6 outcomes (1 - 6). So \( P(3)=\frac{1}{6} \).

Step3: Multiply probabilities (independent events)

For independent events, \( P(A \text{ and } B)=P(A)\times P(B) \). Thus, \( P(\text{heads and } 3)=\frac{1}{2}\times\frac{1}{6}=\frac{1}{12} \).

Answer:

\(\frac{1}{12}\)