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%.
