Marks will be awarded for accuracy in the rounding of final answers where you are asked to round. To ensure that you receive these marks, take care in keeping more decimals in your intermediate steps than what the question is asking you to round your final answer to. A fair 7 -sided die with the numbers 1 trough 7 is rolled five times. Express each of your answers as a decimal rounded to 3 decimal places. (a) What is the probability that exactly one 3 is rolled? (b) What is the probability that at least one 3 is rolled? (c) What is the probability that exactly four of the rolls show an even number?

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Marks will be awarded for accuracy in the rounding of final answers where you are asked to round. To ensure that you receive these marks, take care in keeping more decimals in your intermediate steps than what the question is asking you to round your final answer to.  A fair 7 -sided die with the numbers 1 trough 7 is rolled five times. Express each of your answers as a decimal rounded to 3 decimal places.  (a) What is the probability that exactly one 3 is rolled?  (b) What is the probability that at least one 3 is rolled?  (c) What is the probability that exactly four of the rolls show an even number?

Talisha · Accepted Answer

Data analysis  Given a fair 7-sided die with numbers 1 to 7.  It is rolled 5 times.  So total number of outcomes =75  as one time rolled can give any number from 1 to 7 ⇒ 7 out comes  So five time rolled =75=16.807  To find the following probabilities.  Sub part a)  Probability that exactly one 3 is rolled.   One 3 can come in any of the 5 rolls ⇒ 5 ways  And in remaining 4 rolls, any outcome can come ⇒74 ways  Total favourable ways =5 × 74  Probability =(5 × 74)/75  =5/7  Hence the probability that only one 3 is rolled is 0.714  (Rounded to 3 decimals)  Sub part b)  Probability that at least one 3 is rolled  =1 − (probability of 3 is never rolled)  So 3 should never come ⇒ possible outcomes are 1, 2, 4, 5, 6, 7  Number of ways =6  For five time rolls =56  Probability =1 − (56/57)  =1 − (1/5)  =4/5  Hence the probability that atleast one three is rolled is 0.8  Sub part c)  Probability that exactly 4 of the rolls show even number.  Even number ⇒ 2, 4, 6, ⇒ 3 outcomes  So 4 rolls even =43 ways  And remaining one roll in 7 ways  Total favourable ways =7 × 43  Probability =(7 × 43)/75  (= 64/2401  Hence the probability that exactly 4 of the rolls show even number.   (Rounded to 3 decimals)

Marks will be awarded for accuracy in the rounding of final answers where you are asked to round. To ensure that you receive these marks, take care in

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