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Chapter 11: Problem 23

In Exercises 23-24, a coin is tossed and a die is rolled. Find the probability of getting a head and a number greater than 4 .

Short Answer

Expert verified
The probability is 1/6.

Step by step solution

01

Calculate Probability of Each Individual Event

The individual events are independent, meaning they do not affect each other's outcomes. Therefore, the probability of each event can be calculated individually. When a coin is tossed, there are two possible equally likely outcomes: head or tail. Therefore, the probability of getting a head, \( P(H) \), is 1/2. A standard die has six faces, numbered from 1 to 6. There are two numbers greater than 4: 5 and 6. Therefore, the probability of rolling a number greater than 4, \( P(>4) \), is 2/6 = 1/3.
02

Calculate Joint Probability

Then, calculate the joint probability of these two independent events happening simultaneously. The Joint probability of two independent events is calculated by multiplying their individual probabilities. It's represented as \( P(A and B) = P(A) * P(B) \). Here A stands for the event 'getting a head when tossing a coin' and B stands for the event 'rolling a number greater than 4'. Hence, \( P(H and >4) = P(H) * P(>4) = 1/2 * 1/3 = 1/6 \).
03

State the Answer

The probability of getting a head in the coin toss and rolling a number greater than 4 on the six-sided die is 1/6.

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