A cereal manufacturer includes a collectible card in some of its cereal boxes. For a specific promotion, a card is placed in 30% of the boxes. No box contains more than 1 card. The boxes are sold in multipacks of 8 boxes.
(i) Write down a suitable distribution to model the number of cards found in a multipack. (ii) Write down one assumption required for the model.
Find the probability that in 2 randomly selected multipacks, exactly 1 multipack contains exactly 2 cards.
Find the probability that a randomly selected multipack contains at least 3 cards.
An organizer buys 100 multipacks for a school event.
Using a normal approximation, find the probability that more than 40 of these multipacks contain at least 3 cards.
