Random experiments and sample spaces
Answers are for parents and teachers.
1
A coin is tossed, and then one letter card is drawn from a bag holding the cards A, B and C. List S and give n(S).
S = {(H, A), (H, B), (H, C), (T, A), (T, B), (T, C)}; n(S) = 2 × 3 = 6.
2
Two dice are rolled. Write the event “the difference between the two numbers is 4” as a set of pairs, and say how many it has.
{(1, 5), (2, 6), (5, 1), (6, 2)}: 4 pairs.
3
A bag holds six tiles numbered 1 to 6. Two are drawn without replacement. How many outcomes does S have? List the outcomes of the event “the sum is 7”.
n(S) = 6 × 5 = 30. Sum 7: (1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3): 6 outcomes.
4
Three coins are tossed. Write the events (a) “both a head and a tail appear” and (b) “at most one tail” and give the number of outcomes of each.
(a) all outcomes except HHH and TTT: {HHT, HTH, HTT, THH, THT, TTH}, 6 outcomes. (b) {HHH, HHT, HTH, THH}: 4 outcomes.
5
For one die say whether each event is simple, sure or impossible: (a) a number greater than 6, (b) a number from 1 to 6, (c) the number 2.
(a) impossible, ∅; (b) sure, S; (c) simple, {2}.