Questions: Question 5 A die is rolled. Find the probability of the given event. (a) The number showing is a 5 ; The probability is : (b) The number showing is an even number; The probability is : (c) The number showing is greater than 1 ; The probability is:

Question 5 A die is rolled. Find the probability of the given event. (a) The number showing is a 5 ; The probability is : (b) The number showing is an even number; The probability is : (c) The number showing is greater than 1 ; The probability is:

Solution

Solution Steps

Step 1: Identify the Type of Event

The event is to find the probability of the die showing a specific number: 5.

Step 2: Apply the Probability Formula for a Specific Number

Since there are 6 possible outcomes and each outcome is equally likely, the probability \(P\) of the die showing the number 5 is calculated as \(P = \frac{1}{6}\).

Final Answer:

The probability of the die showing the number 5 is \(P = 0.17\).

Step 1: Identify the Type of Event

The event is to find the probability of the die showing an even number.

Step 2: Apply the Probability Formula for Even Numbers

Since there are exactly three even numbers (2, 4, 6) on a six-sided die, the probability \(P\) is calculated as \(P = \frac{3}{6} = \frac{1}{2}\).

Final Answer:

The probability of the die showing an even number is \(P = {P}\).

Step 1: Identify the Type of Event

The event is to find the probability of the die showing a number greater than 1.

Step 2: Determine the Count of Numbers Satisfying the Condition

There are 5 numbers on a six-sided die that are greater than 1.

Step 3: Apply the Probability Formula for Numbers Greater Than a Certain Value

The probability \(P\) is calculated as \(P = \frac{5}{6}\).

Final Answer:

The probability of the die showing a number greater than 1 is \(P = 0.83\).

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