Probability and Statistics 1 - Paper 5

Worked examples (12)extended set

• 1Drawing a back-to-back stem-and-leaf diagram
• 2Reading a given back-to-back diagram and comparing
• 3Choosing a suitable representation
• 4Box-and-whisker plots with an outlier
• 5Histogram with rounded, unequal classes
• 6Reading frequencies back from a histogram
• 7Cumulative frequency graph from rounded data
• 8Cumulative table, 'more than' and the mean
• 9Box plot and proportions from a given cumulative frequency graph
• 10Completing a histogram with no vertical scale
• 11Cumulative frequency meets the normal and binomial
• 12Stem-and-leaf with unknown leaves

Worked examples (13)extended set

• 1Averages, spread and an outlier
• 2Standard deviation from a raw list
• 3Median and IQR from a stem-and-leaf diagram
• 4Every measure from a discrete frequency table
• 5SD from Σx and Σx², then adding values
• 6Coded totals: find the code, then the SD
• 7Grouped mean and SD from a cumulative table
• 8Combining two groups given means and SDs
• 9Missing frequency from a given mean
• 10Changing units, then correcting a value
• 11Reverse problem: find Σy² from a combined SD
• 12Two unknown values from the mean and variance
• 13Combining coded summaries, then a normal model

Worked examples (13)extended set

• 1Flags on a pole: only the colours matter
• 2People in a line: next to each other or not
• 3Choosing a team: exactly, at least one, include and exclude
• 4TENNESSEE: blocks, gaps and
• 5PEPPERMINT: fixed ends and letters between a pair
• 6Boys and girls in a line: blocks, gaps and alternating
• 7Two rows for a photograph
• 8Four-digit numbers from digit cards
• 9Panel of experts: listing scenarios
• 10BALLERINA: selections with repeated letters
• 11MEMORISE: a letter inside the gap, and at least k between
• 12Splitting volunteers into groups
• 13PAPAYAS: arrangements and repeated draws

Worked examples (13)extended set

• 1Spinner and die: independent and exclusive events
• 2Probabilities from a Venn diagram of counts
• 3Two games where the second depends on the first
• 4Exclusive versus independent from given probabilities
• 5Two-way table: union, independence and conditionals
• 6Three sweets without replacement: counting the orders
• 7Moving a ball from one bag to another
• 8Replaced on one colour, kept on the other
• 9Biased coin chooses the box, then two marbles
• 10A game that stops at the first hit
• 11Unknown number of red counters from a probability
• 12Three dice, given at least one six
• 13Which machine made the faulty item?

Worked examples (13)extended set

• 1Probabilities defined by a formula
• 2Binomial: building p and reading the success criteria
• 3Geometric: on, before and after the r-th trial
• 4Three players with different probabilities
• 5Counters drawn without replacement
• 6Drawing until the first green counter
• 7Product of scores on two spinners
• 8Finding n and p from the mean and variance
• 9Finding p for a geometric model, then the smallest n
• 10The r-th success on the n-th trial
• 11Probability from an arrangement, then repeated shuffles
• 12Unknown probabilities from a given mean
• 13Normal probability feeding a binomial and a geometric

Worked examples (12)extended set

• 1Probability between two values when the variance is given
• 2Expected number of days within a given distance of the mean
• 3Finding σ from a critical percentage, then a value exceeded by 5%
• 4Finding μ from a 'greater than' percentage
• 5Finding μ and σ from two tail areas on a diagram
• 6Two values that both lie below the mean
• 7Symmetry, then σ, then a 'k standard deviations' probability
• 8Justify and use the normal approximation to the binomial
• 9Exact binomial for a small sample, approximation for a large one
• 10A normal percentage feeding an exact and an approximate binomial
• 11Finding σ, then a geometric 'first occasion' question
• 12Show that μ = kσ, then solve and criticise the model