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?

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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?

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Answer 1 · 2018-06-11T20:21:08

Probability of a male being surveyed: $\frac{21}{40}$ $21/40$

Probability of person having cell phone: $\frac{13}{32}$ $13/32$

Probability of being a male with a cell phone: $\frac{5}{13}$ $5/13$

Explanation:

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

$\frac{420}{800}$ $420/800$

Now simplify the fraction:

$\frac{21}{40}$ $21/40$

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:

$\frac{325}{800} = \frac{13}{32}$ $325/800= 13/32$

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

$325 - 200 = 125$ $325-200=125$

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

$\frac{125}{325} = \frac{5}{13}$ $125/325=5/13$

Hope this helps!

Answer 2 · 2018-06-13T22:38:33

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

Explanation:

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

Then:

$P (M \cup C) = P (M) + P (C) - P (M \cap C)$ $"P"(M uu C) = "P"(M) + "P"(C) - "P"(M nn C)$

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

$P (M) = \frac{420}{800}$ $"P"(M) = 420/800$

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

$P (C) = \frac{325}{800}$ $"P"(C) = 325/800$

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

$P (M \cap C) = \frac{125}{800}$ $"P"(M nn C) = 125/800$

Putting it all together:

$P (M \cup C) = P (M) + P (C) - P (M \cap C)$ $"P"(M uu C) = "P"(M) + "P"(C) - "P"(M nn C)$

$P (M \cup C) = \frac{420}{800} + \frac{325}{800} - \frac{125}{800}$ $color(white)("P"(M uu C)) = 420/800 + 325/800 - 125/800$

$P (M \cup C) = \frac{620}{800}$ $color(white)("P"(M uu C)) = 620/800$

$P (M \cup C) = \frac{31}{40} = 77.5 %$ $color(white)("P"(M uu C)) = 31/40" " = 77.5%$

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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?

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