Respuesta :
Answer:
For x = 0, P(x = 0) = 0.35
For x = 1, P(x = 1) = 0.54
For x = 2, P(x = 2) = 0.11
For x = 3, P(x = 3) = 0
Step-by-step explanation:
We are given that the Sky Ranch is a supplier of aircraft parts. Included in stock are 6 altimeters that are correctly calibrated and two that are not. Three altimeters are randomly selected, one at a time, without replacement.
Let X = the number that are not correctly calibrated.
Number of altimeters that are correctly calibrated = 6
Number of altimeters that are not correctly calibrated = 2
Total number of altimeters = 6 + 2 = 8
(a) For x = 0: means there are 0 altimeters that are not correctly calibrated.
This means that all three selected altimeters are correctly calibrated.
Total number of ways of selecting 3 altimeters from a total of 8 = [tex]^{8}C_3[/tex]
The number of ways of selecting 3 altimeters from a total of 6 altimeters that are correctly calibrated = [tex]^{6}C_3[/tex]
So, the required probability = [tex]\frac{^{6}C_3}{^{8}C_3}[/tex]
= [tex]\frac{20}{56}[/tex] = 0.35
(b) For x = 1: means there is 1 altimeter that is not correctly calibrated.
This means that from three selected altimeters; 1 is not correctly calibrated and 2 are correctly calibrated.
Total number of ways of selecting 3 altimeters from a total of 8 = [tex]^{8}C_3[/tex]
The number of ways of selecting 2 correctly calibrated altimeters from a total of 6 altimeters that are correctly calibrated = [tex]^{6}C_2[/tex]
The number of ways of selecting 1 not correctly calibrated altimeters from a total of 2 altimeters that are not correctly calibrated = [tex]^{2}C_1[/tex]
So, the required probability = [tex]\frac{^{6}C_2 \times ^{2}C_1 }{^{8}C_3}[/tex]
= [tex]\frac{30}{56}[/tex] = 0.54
(c) For x = 2: means there is 2 altimeter that is not correctly calibrated.
This means that from three selected altimeters; 2 are not correctly calibrated and 1 is correctly calibrated.
Total number of ways of selecting 3 altimeters from a total of 8 = [tex]^{8}C_3[/tex]
The number of ways of selecting 1 correctly calibrated altimeters from a total of 6 altimeters that are correctly calibrated = [tex]^{6}C_1[/tex]
The number of ways of selecting 2 not correctly calibrated altimeters from a total of 2 altimeters that are not correctly calibrated = [tex]^{2}C_2[/tex]
So, the required probability = [tex]\frac{^{6}C_1 \times ^{2}C_2 }{^{8}C_3}[/tex]
= [tex]\frac{6}{56}[/tex] = 0.11
(d) For x = 3: means there is 3 altimeter that is not correctly calibrated.
This case is not possible, so this probability is 0.
