IB Mathematics Analysis and Approaches Topic SL…

A bag contains 8 marbles: 3 red, 3 blue, and 2 green. A game involves drawing marbles without replacement until either two marbles of the same color are drawn consecutively or all marbles are drawn. Let $Y$ be the number of draws when the game ends.

(a) Find the probability that the first two draws yield marbles of the same color.

(b) Find the probability that the game ends on the third draw due to drawing two consecutive marbles of the same color.

(c) the probability distribution of $Y$ for $Y=2,3,4$ , given that the game ends on or before the fourth draw due to drawing two consecutive marbles of the same color.

A store sells three types of drinks: cola (C), juice (J), and water (W). A survey of 80 customers shows that 45 buy cola, 40 buy juice, 30 buy water, 20 buy both cola and juice, 15 buy both cola and water, 10 buy both juice and water, and 5 buy all three.

(a) Complete the Venn diagram for drink purchases.

(b) Find the probability that a randomly chosen customer buys at least two types of drinks.

A box contains 10 marbles: 4 red (R), 3 blue (B), and 3 green (G). Two marbles are drawn randomly without replacement.

(a) Write down the probability that the first marble drawn is red.

(b) Find the probability that the second marble drawn is blue, given that the first marble drawn was green.

A bag contains 12 cards labeled with the numbers 1 to 12. Three cards are drawn randomly without replacement.

(a) Find the probability that the first card drawn is even-numbered.

(b) Find the probability that the second card drawn is odd-numbered given that the first card was even-numbered.

A travel agency organizes trips to three destinations: Paris (P), Tokyo (T), and New York (N). A survey of 150 clients shows:

80 visited Paris, 70 visited Tokyo, 60 visited New York.
40 visited both Paris and Tokyo, 30 visited both Paris and New York, 20 visited both Tokyo and New York.
10 visited all three.

In a raffle, a client receives $100$ per destination visited; if they visited none, they pay a $50$ fee. Let $W$ be the prize amount.

(a) a Venn diagram for the destinations visited.

(b) Show that the number of clients who visited none of the destinations is $20$ .

(d) the expected value of $Y$ given this distribution.

(d) the expected value of $W$ .

(e) Find the probability that a client visited Tokyo given they visited at least two destinations.

IB Mathematics Analysis and Approaches SL 4.5—probability Concepts, Expected Numbers Questionbank

IB Mathematics Analysis and Approaches SL 4.5—probability Concepts, Expected Numbers Questionbank

IB Mathematics Analysis and Approaches SL 4.5—probability Concepts, Expected Numbers Questionbank

IB Mathematics Analysis and Approaches SL 4.5—probability Concepts, Expected Numbers Questionbank

IB Mathematics Analysis and Approaches (AA) Topic SL 4.5—probability Concepts, Expected Numbers Questionbank