Question

1. you toss a coin and roll a number cube. find p (tail and a six).

Explanation:

Step1: Calculate the probability of getting a tail

The probability of getting a tail when tossing a coin is \(P(\text{tail})=\frac{1}{2}\) since there are 2 possible outcomes (head or tail) and 1 favorable outcome (tail).

Step2: Calculate the probability of getting a six on a number cube

A standard number cube has 6 faces numbered from 1 to 6. The probability of getting a six is \(P(6)=\frac{1}{6}\) as there is 1 favorable outcome (the face with 6) out of 6 possible outcomes.

Step3: Use the formula for the probability of independent events

Since the coin - toss and the number - cube roll are independent events, the formula \(P(A\cap B)=P(A)\times P(B)\) is used. Here, \(A\) is the event of getting a tail and \(B\) is the event of getting a six.
So, \(P(\text{tail and }6)=\frac{1}{2}\times\frac{1}{6}\)

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Answer:

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