In this lesson:
You will be able to:
A random employee works full-time?
"Suppose it rained today. What is the probability you brought an umbrella?" is not the same as "...on any random day?"
Notation: = "the probability of , given that has occurred"
The sample space shrinks to the outcomes where is true.
Recall: of the 120 part-time, are satisfied: now .
Rule: "Given that..." → find that group's total → use as denominator.
: given full-time → 180; satisfied → 120
: given not satisfied → 130; part-time → 70
The 300s cancel: the formula and the restricted column agree.
The same numerator (120) — but different denominators (180 and 170): and .
These phrases signal a conditional question:
Strategy: Underline the phrase. That group = denominator.
On the employee table, one employee is chosen at random from the full-time employees. What is the probability that the employee is satisfied?
A) B) C) D)
Answer: C, . D is . A is . B is .
"Of the part-time employees, what fraction are not satisfied?"
"If an employee who reported not being satisfied is chosen at random, what is the probability the employee works full-time?" →
Contrast: a random employee is a satisfied part-time worker? No "given" → grand total:
The part-time column totals . The satisfied part-time cell is blank, but .
The given group's total times the conditional probability gives the count.
A club has 40 members, 25 of them juniors. Of the juniors, 10 play chess.
A junior is chosen: , not .
Never use grand total for conditional P
Underline the given phrase to find the denominator
Next topic in the sequence: Compound events (and, or, complement)
Today's skill carries over: name the denominator group before you compute.