a) To calculate the probability that 3 iPhones and 3 Samsung Galaxy phones will be repaired, we need to use the hypergeometric distribution.
The total number of dysfunctional iPhones is 10, and the total number of dysfunctional Samsung Galaxy phones is 12. The total number of dysfunctional phones is 22.
We want to calculate the probability of selecting 3 iPhones and 3 Samsung Galaxy phones, so we choose 3 from the 10 iPhones and 3 from the 12 Samsung Galaxy phones.
The probability is given by the formula:
P(3 iPhones and 3 Samsung Galaxy phones) = (10 choose 3) * (12 choose 3) / (22 choose 6)
Using combinatorial notation, this can be expressed as:
P(3 iPhones and 3 Samsung Galaxy phones) = (10C3) * (12C3) / (22C6)
Calculating this will give us the probability.
b) To calculate the probability that at most 4 Samsung Galaxy phones will be repaired, we need to add up the probabilities of selecting 0, 1, 2, 3, and 4 Samsung Galaxy phones that will be repaired.
For each case, we use the hypergeometric distribution to calculate the probability.
The probability of selecting 0 Samsung Galaxy phones that will be repaired is given by:
P(0 Samsung Galaxy phones repaired) = (10 choose 6) * (12 choose 0) / (22 choose 6)
Similarly, the probabilities for selecting 1, 2, 3, and 4 Samsung Galaxy phones that will be repaired can be calculated using the hypergeometric distribution.
Finally, we add up all these probabilities to get the probability of having at most 4 Samsung Galaxy phones repaired.
smartphone repair company received 10 dysfunctional iPhones and 12 dysfunc-
tional Samsung Galaxy phones. Assuming that the company will repair only 6 devices that
are selected randomly, calculate the following probabilities
a) 3 iPhones and 3 Samsung Galaxy phones will be repaired.
b) At most 4 Samsung Galaxy phones will be repaired.
1
1 answer