select the correct answer.\na company that manufactures smartphones makes 70% of the phones with a touch…

select the correct answer.\na 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?\na. $\frac{19}{20}$\nb. $\frac{47}{50}$\nc. $\frac{13}{20}$\nd. $\frac{43}{50}$\ne. $\frac{17}{20}$

select the correct answer.\na 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?\na. $\frac{19}{20}$\nb. $\frac{47}{50}$\nc. $\frac{13}{20}$\nd. $\frac{43}{50}$\ne. $\frac{17}{20}$

Answer

Explanation:

Step1: Recall the formula for the probability of the union of two events

Let $A$ be the event that a phone has a touch - screen and $B$ be the event that a phone has HD movie capability. The formula for $P(A\cup B)$ is $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.

Step2: Identify the given probabilities

We are given that $P(A) = 0.7$, $P(B)=0.55$, and $P(A\cap B)=0.3$.

Step3: Substitute the values into the formula

$P(A\cup B)=0.7 + 0.55-0.3$. $P(A\cup B)=0.95$.

Step4: Convert the decimal to a fraction

$0.95=\frac{95}{100}=\frac{19}{20}$.

Answer:

A. $\frac{19}{20}$