Binomial Distributions
- A fair six-sided die is rolled six times. Which of the following is/are given by
?
A: The probability of getting exactly one 2 .
B: The probability of getting exactly two 1 s .
C: The probability of getting exactly four 5 s .
D: The probability of getting exactly five 4 s .
E: The probability of getting exactly two scores less than 6.
F: The probability of getting exactly four scores greater than 1 .
2. A discrete random variable X is modelled by the binomial distribution. Khunsha uses the binomial cumulative probability feature of her calculator to find
Which one of the following is the same as
B: The probability of getting exactly two 1 s .
C: The probability of getting exactly four 5 s .
D: The probability of getting exactly five 4 s .
E: The probability of getting exactly two scores less than 6.
F: The probability of getting exactly four scores greater than 1 .
2. A discrete random variable X is modelled by the binomial distribution. Khunsha uses the binomial cumulative probability feature of her calculator to find
Which one of the following is the same as
Explain your answer.
3. The probability that Annie hits the target with a shot is 0.28 . Find the least number of shots Annie must fire so that the probability of at least one successful shot is greater than 0.99.
4. The probability that a newborn baby is a boy is 0.52 . Find the probability that in a family of 6 children there are more girls than boys.
5. A discrete random variable
6. The random variable X represents the score after a single roll of a biased six-sided die for which
(a) Find the value of the constant
(b) The die is rolled 20 times. Calculate the probability that the score is greater than 4 on more than half of the rolls.
7. Every weekday Mr Bullar, a teacher, leaves home early in the hope that his favourite car parking spot is available at school. On average he finds that he gets this spot on one day out of three. Let the random variable X represent the number of days in a working week of 5 days that Mr Bullar parks in his favourite spot.
(a) In order to use a binomial distribution model for X , state one assumption you will need to make.
(b) Calculate the probability that Mr Bullar parks in his favourite spot on at least 2 weekdays in a given week.
3. The probability that Annie hits the target with a shot is 0.28 . Find the least number of shots Annie must fire so that the probability of at least one successful shot is greater than 0.99.
4. The probability that a newborn baby is a boy is 0.52 . Find the probability that in a family of 6 children there are more girls than boys.
5. A discrete random variable
6. The random variable X represents the score after a single roll of a biased six-sided die for which
(a) Find the value of the constant
(b) The die is rolled 20 times. Calculate the probability that the score is greater than 4 on more than half of the rolls.
7. Every weekday Mr Bullar, a teacher, leaves home early in the hope that his favourite car parking spot is available at school. On average he finds that he gets this spot on one day out of three. Let the random variable X represent the number of days in a working week of 5 days that Mr Bullar parks in his favourite spot.
(a) In order to use a binomial distribution model for X , state one assumption you will need to make.
(b) Calculate the probability that Mr Bullar parks in his favourite spot on at least 2 weekdays in a given week.
There are seven school weeks in the next half term. Mr Bullar thinks it’s a good week if he parks in his favourite spot on more than one day in the week, otherwise he calls it a bad week.
