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A company that manufactures smartphones makes 70% of the phones with a touch screen and 55% of the phones with HD movie capability. 30% of the phones have both a touch screen and HD movie capability. What is the probability that a smartphone chosen at random has either a touch screen or HD movie capability?

A company that manufactures smartphones makes 70 of the phones with a touch screen and 55 of the phones with HD movie capability 30 of the phones have both a to class=

Respuesta :

akaleti47
.7+.55-.3=1.25-.3=.95=95/100=19/20 thats the first option

Answer:

Option: A is the correct answer.

[tex]\dfrac{19}{20}[/tex]

Step-by-step explanation:

A company manufactures 70% touch screen phones.

55% have HD capability.

and 30% have both touch screen and HD capability.

Let A denote the touch screen phones.

B denote the HD capability.

C denote the both touch and HD capability.

Now we are asked to find the probability that a smartphone chosen at random has either a touch screen or HD movie capability:

i.e.. we have to find P(A∪B)

we know that:

P(A∪B)=P(A)+P(B)-P(A∩B)

Hence,

[tex]P(A\bigcup B)=\dfrac{70}{100}+\dfrac{55}{100}-\dfrac{30}{100}\\\\P(A\bigcup B)=\dfrac{95}{100}=\dfrac{19}{20}[/tex]

Hence, option: A is correct.

[tex]\dfrac{19}{20}[/tex]

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