Question

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

Answer 1

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 2

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.