Question

name________
ib applications year 1 graded hw - probability (12 marks)
srinivasa places the nine labelled balls shown below into a box.
r a m a n u j a n
srinivasa then chooses two balls at random, one at a time, from the box. the first ball is not replaced before he chooses the second.
a. i. find the probability that the first ball chosen is labelled a. 1
ii. find the probability that the first ball chosen is labelled a or labelled n. 1
b. find the probability that the second ball chosen is labelled a, given that the first ball chosen was labelled n. 2
c. find the probability that both balls chosen are labelled n. 2

Explanation:

Step1: Count total and A balls

Total balls = 9, Number of A balls = 3
Probability = $\frac{\text{Number of A balls}}{\text{Total balls}}$
$P(\text{first is A}) = \frac{3}{9} = \frac{1}{3}$

Step2: Count A or N balls

Number of N balls = 2, Number of A or N balls = $3+2=5$
Probability = $\frac{\text{Number of A/N balls}}{\text{Total balls}}$
$P(\text{first is A or N}) = \frac{5}{9}$

Step3: Conditional probability (A after N)

After removing 1 N, total balls = 8, A balls remain 3
$P(\text{second is A}|\text{first is N}) = \frac{3}{8}$

Step4: Probability both are N

First N: $\frac{2}{9}$, Second N (after first N removed): $\frac{1}{8}$
$P(\text{both N}) = \frac{2}{9} \times \frac{1}{8}$

Answer:

a. i. $\boldsymbol{\frac{1}{3}}$
a. ii. $\boldsymbol{\frac{5}{9}}$
b. $\boldsymbol{\frac{3}{8}}$
c. $\boldsymbol{\frac{1}{36}}$