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Suppose a fair die is tossed once. Find the probability of: a) obtaining the number 5, b) obtaining the number 8, c) obtaining an even number, d) obtaining an odd number.

Mathematics

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Answers

4 parts
a

16\frac{1}{6}

b
0
c

12\frac{1}{2}

d

12\frac{1}{2}

Step-by-step solution

8 steps

let's solve this die problem.

When a fair die is tossed once, the sample space (all possible outcomes) is:

S={1,2,3,4,5,6}S = \{1, 2, 3, 4, 5, 6\}

The total number of possible outcomes is n(S)=6n(S) = 6.

Part a· 2 steps

obtaining the number 5

  1. Count the number of times '5' appears in the sample space.

    The number 5 appears 1 time.

  2. Calculate the probability.

    P(obtaining 5)=Number of times 5 appearsTotal number of outcomes=16P(\text{obtaining 5}) = \frac{\text{Number of times 5 appears}}{\text{Total number of outcomes}} = \frac{1}{6}

    The probability of obtaining the number 5 is 16\boxed{\frac{1}{6}}.

Part b0

obtaining the number 8

  1. Count the number of times '8' appears in the sample space.

    The number 8 does not appear on a standard fair die. So, it appears 0 times.

  2. Calculate the probability.

    P(obtaining 8)=Number of times 8 appearsTotal number of outcomes=06=0P(\text{obtaining 8}) = \frac{\text{Number of times 8 appears}}{\text{Total number of outcomes}} = \frac{0}{6} = 0

    The probability of obtaining the number 8 is 0\boxed{0}.

Part c

12\frac{1}{2}

obtaining an even number

  1. Identify and count the even numbers in the sample space.

    The even numbers are $2, 4, 6$. There are 3 even numbers.

  2. Calculate the probability.

    P(obtaining an even number)=Number of even numbersTotal number of outcomes=36=12P(\text{obtaining an even number}) = \frac{\text{Number of even numbers}}{\text{Total number of outcomes}} = \frac{3}{6} = \frac{1}{2}

    The probability of obtaining an even number is 12\boxed{\frac{1}{2}}.

Part d

12\frac{1}{2}

obtaining an odd number

  1. Identify and count the odd numbers in the sample space.

    The odd numbers are $1, 3, 5$. There are 3 odd numbers.

  2. Calculate the probability.

    P(obtaining an odd number)=Number of odd numbersTotal number of outcomes=36=12P(\text{obtaining an odd number}) = \frac{\text{Number of odd numbers}}{\text{Total number of outcomes}} = \frac{3}{6} = \frac{1}{2}

    The probability of obtaining an odd number is 12\boxed{\frac{1}{2}}.

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