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?

2 Answers
Jun 11, 2018

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!

Jun 13, 2018

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%