Question

Of 800 people surveyed, 420 were male, and 325 had cell phones. Of those with cell phones, 200 were female. What is the probability that a person surveyed was either male or had a cell phone?

Answer 1

Probability of a male being surveyed: `21/40`

Probability of person having cell phone: `13/32`

Probability of being a male with a cell phone: `5/13`

Explanation:

`420` males were surveyed. To find the probability that a person was surveyed and is a male, you have to put `420` as the numerator and `800` as the denominator. The reason you have to do this is because `420` males were surveyed out of `800` people. “ Out of ” can be translated as the denominator.

`420/800`

Now simplify the fraction:

`21/40`

This is the probability of surveying a male.

Now, let’s find the probability of surveying a person with a cell phone. We do the same process as above:

`325/800= 13/32`

The probability of surveying a male with a cellphone:
`200` woman have cellphones so we have to subtract them from the `325` people who have cellphones so we can find out how many males have a cellphone

`325-200=125`

So `125` males have cellphones. Let’s do same process as we have done the past two probabilities:

`125/325=5/13`

Hope this helps!

Answer 2

The probability is 31/40, or 0.775 (77.5%).

Explanation:

Let `M` stand for "the person surveyed was male".
Let `C` stand for "the person surveyed had a cell phone".

Then:

`"P"(M uu C) = "P"(M) + "P"(C) - "P"(M nn C)`

Of the 800 people surveyed, the number of people who are male is 420. Thus,

`"P"(M) = 420/800`

Of the 800 people surveyed, the number of people who have a cell phone is 325. Thus,

`"P"(C) = 325/800`

Of the 325 people who have cell phones, 200 are female. This means the remaining 125 people with cell phones are male. Thus,

`"P"(M nn C) = 125/800`

Putting it all together:

`"P"(M uu C) = "P"(M) + "P"(C) - "P"(M nn C)`

`color(white)("P"(M uu C)) = 420/800 + 325/800 - 125/800`

`color(white)("P"(M uu C)) = 620/800`

`color(white)("P"(M uu C)) = 31/40" " = 77.5%`