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3. A smartphone repair company received 10 dysfunctional iPhones and 12 dysfunctional 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.

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Solution:-

3)

a) The probability that 3 Iphones and 3 Samsung Galaxy phones will be repaired is 0.3538.

Total number of ways of selecting 6 devices = 22C6 = 74613

Number of ways to select 3 Iphones and 3 Samsung Galaxy phones = 10C3*12C3 = 120*220 = 26,400

The probability that 3 Iphones and 3 Samsung Galaxy phones will be repaired = 26400/74613

The probability that 3 Iphones and 3 Samsung Galaxy phones will be repaired = 0.3538.

b) The probability that atmost 4 samsung galaxy phones will be repaired is 0.8815.

Number of ways to select atmost 4 samsung galaxy phones phones = 10C2*12C4 +10C3*12C3 + 10C4*12C2 + 10C5*12C1 + 10C6*12C0= 45*495 + 120*220 + 210*66 + 252*12 = 22275 + 26400 + 13860 + 3024 + 210 = 65769.

Total number of ways of selecting 6 devices = 22C6 = 74613

The probability that atmost 4 samsung galaxy phones will be repaired = 65769/74613 = 0.8815.

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