Answer :
To solve this problem, we're looking for the probability that a smartphone chosen at random has either a touch screen or HD movie capability. We are given the following probabilities:
- Probability of a phone with a touch screen, [tex]\( P(T) = 70\% = 0.70 \)[/tex]
- Probability of a phone with HD movie capability, [tex]\( P(H) = 55\% = 0.55 \)[/tex]
- Probability of a phone having both features, [tex]\( P(T \text{ and } H) = 30\% = 0.30 \)[/tex]
To find the probability of a smartphone having either a touch screen or HD movie capability, we use the formula for the union of two events:
[tex]\[ P(T \text{ or } H) = P(T) + P(H) - P(T \text{ and } H) \][/tex]
Substitute the given values into the formula:
[tex]\[ P(T \text{ or } H) = 0.70 + 0.55 - 0.30 \][/tex]
Calculate step-by-step:
1. Add the probabilities of the individual events: [tex]\( 0.70 + 0.55 = 1.25 \)[/tex].
2. Subtract the probability of both events occurring: [tex]\( 1.25 - 0.30 = 0.95 \)[/tex].
Thus, the probability that a smartphone has either a touch screen or HD movie capability is [tex]\( 0.95 \)[/tex].
To express this as a fraction and locate the correct answer from the choices, we convert [tex]\( 0.95 \)[/tex] to a fraction. The equivalent fraction in simplest form is [tex]\(\frac{19}{20}\)[/tex].
Therefore, the correct answer is:
A. [tex]\(\frac{19}{20}\)[/tex]
- Probability of a phone with a touch screen, [tex]\( P(T) = 70\% = 0.70 \)[/tex]
- Probability of a phone with HD movie capability, [tex]\( P(H) = 55\% = 0.55 \)[/tex]
- Probability of a phone having both features, [tex]\( P(T \text{ and } H) = 30\% = 0.30 \)[/tex]
To find the probability of a smartphone having either a touch screen or HD movie capability, we use the formula for the union of two events:
[tex]\[ P(T \text{ or } H) = P(T) + P(H) - P(T \text{ and } H) \][/tex]
Substitute the given values into the formula:
[tex]\[ P(T \text{ or } H) = 0.70 + 0.55 - 0.30 \][/tex]
Calculate step-by-step:
1. Add the probabilities of the individual events: [tex]\( 0.70 + 0.55 = 1.25 \)[/tex].
2. Subtract the probability of both events occurring: [tex]\( 1.25 - 0.30 = 0.95 \)[/tex].
Thus, the probability that a smartphone has either a touch screen or HD movie capability is [tex]\( 0.95 \)[/tex].
To express this as a fraction and locate the correct answer from the choices, we convert [tex]\( 0.95 \)[/tex] to a fraction. The equivalent fraction in simplest form is [tex]\(\frac{19}{20}\)[/tex].
Therefore, the correct answer is:
A. [tex]\(\frac{19}{20}\)[/tex]
