MATH SOLVE

2 months ago

Q:
# The probability that someone owns an iPhone is 62%. The probability that someone owns an Apple watch is 15%. The probability someone owns BOTH is 8%. What is the probability that someone owns an iPhone or an Apple Watch?

Accepted Solution

A:

ANSWER

The probability that someone owns an iPhone or an Apple watch is

[tex]P(I \cup \: A) = 69\%[/tex]

or

[tex]P(I \cup \: A) = 0.69[/tex]

EXPLANATION

We were given that, the probability that someone owns an iPhone is

[tex]P(I)=62\%[/tex]

and the probability that someone owns Apple watch is

[tex]P(A)=15\%[/tex]

and the probability that someone owns both is

[tex]P(I \cap \: A) = 8\%[/tex]

Since the intersection is not zero, it means the two events are not mutually exclusive.

The probability that someone owns an iPhone or Apple phone is

[tex]P(I \cup \: A) = P(I) + P(A) - P(I \cap \: A)[/tex]

We substitute the values to get,

[tex]P(I \cup \: A) = 62\% + 15\% - 8\%[/tex]

[tex]P(I \cup \: A) = 69\%[/tex]

The probability that someone owns an iPhone or an Apple watch is

[tex]P(I \cup \: A) = 69\%[/tex]

or

[tex]P(I \cup \: A) = 0.69[/tex]

EXPLANATION

We were given that, the probability that someone owns an iPhone is

[tex]P(I)=62\%[/tex]

and the probability that someone owns Apple watch is

[tex]P(A)=15\%[/tex]

and the probability that someone owns both is

[tex]P(I \cap \: A) = 8\%[/tex]

Since the intersection is not zero, it means the two events are not mutually exclusive.

The probability that someone owns an iPhone or Apple phone is

[tex]P(I \cup \: A) = P(I) + P(A) - P(I \cap \: A)[/tex]

We substitute the values to get,

[tex]P(I \cup \: A) = 62\% + 15\% - 8\%[/tex]

[tex]P(I \cup \: A) = 69\%[/tex]