Assume you roll a die 2 times. What is the probability that you will get exactly one 6?


  1. Home
  2. Math
  3. All Questions
Answer:

 

10
36
 

Step by Step Explanation:
  1. According to the question, a die rolled 2 times
    So, the Sample Space(S) is { (i, j): i, j = 1, 2, 3, 4, 5, 6 }
  2. Total number of outcomes in sample space n(S) = 6 × 6 = 36
  3. Let E be the event that you will get exactly one 6.
    Number of outcomes in which '6' appears only on the first throw = 1 × 5 = 5
    As the die is thrown 2 times, '6' (appearing exactly once) can appear on any of the 2 throws.
    Therefore, the total number of outcomes when 6 appears exactly once, n(E) = 2 × 5 = 10
  4. Probability, P(E) =  
    n(E)
    n(S)
      =  
    10
    36
     
  5. Therefore, the probability of getting exactly one 6 is  
    10
    36
         .

You can reuse this answer
Creative Commons License