GCSE Statistics Binomial Distribution

Which of the following is NOT an assumption of the Binomial distribution?

• All trials must be independent.
• Each trial must be classified as a success or a failure.
• All trials are dependent on each other.
• The number of successes in the trials is counted.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

What is the next row of Pascal's Triangle?

• Who is Pascal?
• 1  7  9  15  15  9  7  1
• I can't add.
• 1  7  21  35  35  21  7  1

Tags

CCSS.HSA.APR.C.5

The probability of winning one of many prizes in a prize draw is 0.05. Ben and Celia each buy a ticket.

What is n for this binomial distribution?

• 0.05

• 0.95

• 2

• 3

The probability of winning one of many prizes in a prize draw is 0.05. Ben and Celia each buy a ticket.

What is p for this binomial distribution?

• 0.05

• 0.95

• 2

• 3

The probability of winning one of many prizes in a prize draw is 0.05. Ben and Celia each buy a ticket.

Find the probability that only one of them wins a prize.

• 0.905

• 0.0025

• 0.9025

• 0.095

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.1

CCSS.HSS.CP.B.7

Arjun rolls three fair dice.

Find the probability that he gets three sixes on the dice.

[You may use (p + q)³ = p³ + 3p²q + 3pq² + q³.]

• 0.00463

• 0.0694

• 0.347

• 0.579

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.1

CCSS.HSS.CP.B.8

The chance of the school bus arriving late in the morning is 1/5. In a five day week, find the probability that the bus is late exactly once. [You may use (p + q)⁵ = p⁵ + 5p⁴q + 10p³q² + 10p²q³ + 5pq⁴ + q⁵.]

• 1 / 3125

• 4 / 625

• 32 / 625

• 128 / 625

• 256/625

Tags

CCSS.HSS.CP.B.9

In a gymnastics competition, each gymnast must perform four routines. For each routine Kieran has a 70% chance of performing without a mistake. Could this be modelled using a binomial distribution?

• 
• 

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.3

CCSS.HSS.CP.B.8

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

In a gymnastics competition, each gymnast must perform four routines. For each routine Kieran has a 70% chance of performing without a mistake. What is the probability that Kieran performs more than two of his routines without a mistake? [(p + q)⁴ = p⁴ + 4p³q + 6p²q² + 4pq³ + q⁴.]

• 0.7354

• 0.4116

• 0.6517

• 0.9163

Tags

CCSS.HSS.CP.B.9

Of the following, select all those for which the binomial distribution might be a suitable model.

• The total score on two fair dice

• The number of heads on six coins when flipped.

• The number of pieces of buttered toast that land butter side up if three pieces of toast are dropped.

• The number of buses passing a bus stop in one hour.

• The weight of five dice that are rolled

Tags

CCSS.HSS.MD.A.2

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.1