Answered

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?


19/20


47/50


13/20


43/50


17/20

Verified Answer :

Justtae16

P(A or B) = P(A) + P(B) - P(A and B)
P(A or B)=0.7+0.55-0.3
P(A or B)= 0.4+0.55
P(A or B)=0.95

Answer:

\(\frac{19}{20}\)

Step-by-step explanation:

Let T represents the event of phones with a touch screen and H represents the event of phones with HD movie capability.

Given,

70% of the phones with a touch screen,

⇒ The probability of touch screen phone, P(T) = 70% = 0.7,

55% of the phones with HD movie capability,

⇒ The probability of HD movie capability phones, P(H) = 55 % = 5.5,

Also, 30% of the phones have both a touch screen and HD movie capability,

⇒ The probability of HD movie capability phones with touch screen,

P(H∩T) = 30 % = 0.3,

Hence, the probability that a smartphone chosen at random has either a touch screen or HD movie capability is,

\(P(H\cup T)= P(H)+P(T)-P(H\cap T)\)

\(=0.7+0.55 - 0.3\)

\(=0.95\)

\(=\frac{95}{100}\)

\(=\frac{19}{20}\)

First option is correct.

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