Respuesta :
Answer: [tex]P(\text{ both the television are working })= 0.65454545 [/tex]
[tex]P(\text{ at least one the two televisions does not work }) =0.34545454545.[/tex]
Explanation:
Since the total number of television= 11
Number of defective television = 2
Remaining television that are working = 9
[tex]P(\text{ both the television are working }) = \frac{ ^9C_2}{^{11}C_2}\\P(\text{ both the television are working })=\frac{9\times 8}{11\times10}\\P(\text{ both the television are working })= \frac{72}{110}\\P(\text{both the television are working })= 0.65454545[/tex]
Now,
[tex]P(\text{ at least one the two televisions does not work }) = 1- \frac{72}{110}\\ P(\text{ at least one the two televisions does not work }) =\frac{110-72}{110}\\P(\text{ at least one the two televisions does not work }) = \frac{38}{110}\\P(\text{ at least one the two televisions does not work }) =0.34545454545.[/tex]
∴ [tex]P(\text{ both the television are working })= \frac{72}{110}[/tex]
[tex]P(\text{ both the television are working })= 0.65454545[/tex]
[tex]P(\text{ at least one the two televisions does not work }) =0.34545454545.[/tex]
The probability at least one of the two televisions does not work is 0.345
Given the following parameters:
total number of television shipped = 11
Defective television = 2
Non defective = 11 - 2 = 9
- Probability is the likelihood or chance that an event will occur.
- Probability = Expected outcome/Total outcome
Pr(two television does not work) = [tex]\frac{9C2}{11C2}[/tex]
[tex]9C2 =\frac{9!}{7!2!}\\9C2 =\frac{9\times 8 \times 7!}{7!2!}\\9C2=\frac{72}{2} = 36[/tex]
Similarly;
[tex]11C2 =\frac{11!}{9!2!}\\11C2 =\frac{11\times 10 \times 9!}{9!2!}\\11C2=\frac{110}{2} = 55[/tex]
- Pr(two television does not work) = [tex]\frac{36}{55}[/tex]
The probability at least one of the two televisions does not work = [tex]1-\frac{36}{55}[/tex]
The probability at least one of the two televisions does not work = [tex]\frac{19}{55} = 0.345[/tex]
Hence the probability at least one of the two televisions does not work is 0.345
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