Coaching Centre
Arrays and tree diagrams
Two-step and three-step experiments using arrays (tables) and tree diagrams, with and without replacement, and relative frequency.
Arrays
Two dice are rolled. Find $P(\text{sum} \ge 10)$.
Tree diagrams
A bag has $4$ red and $6$ blue balls. Two are drawn without replacement. Find $P(\text{one of each colour})$.
Two dice. $P(\text{sum} \ge 10)$?
$6$ of $36$.
$4$ red, $6$ blue, two drawn without replacement. $P(\text{one of each})$?
$\tfrac{48}{90}$.
Same bag. $P(\text{both red})$?
$\tfrac{4}{10} \times \tfrac{3}{9}$.
Same bag, with replacement. $P(\text{both blue})$?
$\tfrac{6}{10} \times \tfrac{6}{10}$.
A coin is tossed and a die rolled. $P(\text{head and } 6)$?
$\tfrac{1}{2} \times \tfrac{1}{6}$.
Three coins are tossed. $P(\text{at least one head})$?
$1 - \tfrac{1}{8}$.
Three coins are tossed. $P(\text{exactly two heads})$?
HHT, HTH, THH: $3$ of $8$.
Two dice. $P(\text{at least one } 6)$?
$1 - \tfrac{25}{36}$.
New numbers every time. Keep going until you get five in a row.