Of the 24 guests invited to Hannah's party, 12 are male and 15 have dark hair. If 7 of the females have dark

Question

Of the 24 guests invited to Hannah's party, 12 are male and 15 have dark hair. If 7 of the females have dark hair. If 7 of the females have dark hair, what is the proability that the first guest to arrive will either have dark hair or be a male?

Be specific please

Appreciate it!

Answer 1

There are 24 guests.
12 are male, so 12 must be female.
15 have dark hair, so 9 do not.

Of the 12 females: 7 have dark hair, 5 do not.
Of the 12 males: 8 have dark hair, 4 do not.

P(male) = 12/24
P(female with dark hair) = 7/24
P(male or dark hair) = 19/24.

This is with the understanding that dark haired males are considered to be "dark haired or male".

Hope that helps!

Answer 2

12/24 = 1/2 are male
15/24 have dark hair
(15-7)/24 = 1/3 are male and have dark hair

So probability that first to arrive (or any random person) will have dark hair OR is a male is:
1/2 + 15/24 - 1/3 = 0.792
The 1/3 is subtracted because males that have dark hair are counted twice in the first 2 terms.

Answer 3

out of 24 guests, 12 are male therefore 12 female. The probability that the 1st person to show up will be male is 12/24=0.5
7 of the 24 are dark haired girls so the probability that the 1st person to show up will be a darkhaired girl is 7/24.
the probability that the 1st person to show up is a boy or a darkhaired girl is therefore 12/24+7/24=19/24 but the question says dark hair OR a male, not &/or. there are 15-7=8 boys have dark hair so the probability that the 1st person to show up is a darkhaired boy is 8/24. The probability that the 1st person to show up will be a boy OR darkhaired BUT NOT BOTH is 19/24-8/24-11/24

Answer 4

This is an inclusion/exclusion principle problem

D: person selected has dark hair
M: person selected is a male

P(D or M) = P(D)+ P(M) - P(D and M)

P(D) = 15/24
P(M) = 12/24
P(D and M) = 8/24

P(D or M) = 15/24 +12/24 - 8/24 = 19/24

Answer 5

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