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?



Answer :

Answer:

To find the probability that a smartphone chosen at random has either a touch screen or HD movie capability, we can use the principle of inclusion and exclusion.

Let \( P(\text{Touch screen}) = 0.7 \), \( P(\text{HD movie}) = 0.55 \), and \( P(\text{Touch screen and HD movie}) = 0.3 \).

The probability that a smartphone has either a touch screen or HD movie capability is given by:

\[

P(\text{Touch screen or HD movie}) = P(\text{Touch screen}) + P(\text{HD movie}) - P(\text{Touch screen and HD movie})

\]

\[

= 0.7 + 0.55 - 0.3

\]

\[

= 0.95 - 0.3

\]

\[

= 0.65

\]

So, the probability that a smartphone chosen at random has either a touch screen or HD movie capability is 0.65, or 65%.