Fifteen telephones have just been received at a cell phone r

Fifteen telephones have just been received at a cell phone repair service and are randomly assigned an order to be repaired. nine of these are iPhones, Four are Samsung phones, and the other two are LG phones including one that is red.

a) What is the probability that two cellphones of each type (iPhone, Samsung, and LG) are among the first six phones serviced?

b) What is the chance that the next phone serviced after the first LG phone is the red LG phone?

c) What is the probability that at least one LG is amongst the first six phones given that four of these six are iPhones

Solution

a) What is the probability that two cellphones of each type (iPhone, Samsung, and LG) are among the first six phones serviced?

Probability of choosing two cell phones of each type = ⁹C₂ * ⁴C₂ * ²C₂ / ¹⁵C₆

= 216 / 5005

= 0.043

c) What is the probability that at least one LG is amongst the first six phones given that four of these six are iPhones.

Probability of having atleast 1LG phone in 6,

= P (Having 1 in 2 phones) + P (Having both LG phones)

= ⁹C₄ * ⁴C₁ * ²C₁ / ¹⁵C₆ + ⁹C₄ * ²C₂ / ¹⁵C₆

= 162 / 715

= 0.2265

.

Note: For the second part, it would be great if you could elaborate on whether the probability to be calculated is for 6 phones chosen earlier or for 15 phones.