SOLUTION: MAT 145: Topics In Contemporary Math More Probability 1) In a recent survey of 200 people, 120 identified themselves as male. Of the 120 males, 60% consider

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Question 1191733: MAT 145: Topics In Contemporary Math

More Probability
1) In a recent survey of 200 people, 120 identified themselves as male. Of the 120 males,
60% considered themselves heterosexual. Of the non-male identifiers, 35% considered
themselves heterosexual. Let M be the event that a person identifies as male and H be the
event that a person considers themselves heterosexual. Use this information to find each
of the following.
๐‘ƒ(๐‘€ ๐‘Ž๐‘›๐‘‘ ๐ป) ๐‘ƒ(๐‘€ ๐‘Ž๐‘›๐‘‘ ๐ป^๐‘)
๐‘ƒ(๐‘€^๐‘ ๐‘Ž๐‘›๐‘‘ ๐ป) ๐‘ƒ(๐‘€๐‘ ๐‘Ž๐‘›๐‘‘ ๐ป^๐‘)
๐‘ƒ(๐ป) P(H^c)
Answer by CPhill(1959) About Me  (Show Source):
You can put this solution on YOUR website!
Here's how to calculate the probabilities:
1. **Number of males (M):** 120
2. **Number of non-males (Mแถœ):** 200 - 120 = 80
3. **Number of heterosexual males (M and H):** 120 * 0.60 = 72
4. **Number of non-heterosexual males (M and Hแถœ):** 120 - 72 = 48
5. **Number of heterosexual non-males (Mแถœ and H):** 80 * 0.35 = 28
6. **Number of non-heterosexual non-males (Mแถœ and Hแถœ):** 80 - 28 = 52
7. **Total number of heterosexual people (H):** 72 + 28 = 100
8. **Total number of non-heterosexual people (Hแถœ):** 48 + 52 = 100
Now, we can calculate the probabilities:
* **P(M and H):** (Number of heterosexual males) / (Total people) = 72 / 200 = 0.36
* **P(M and Hแถœ):** (Number of non-heterosexual males) / (Total people) = 48 / 200 = 0.24
* **P(Mแถœ and H):** (Number of heterosexual non-males) / (Total people) = 28 / 200 = 0.14
* **P(Mแถœ and Hแถœ):** (Number of non-heterosexual non-males) / (Total people) = 52 / 200 = 0.26
* **P(H):** (Total number of heterosexual people) / (Total people) = 100 / 200 = 0.50
* **P(Hแถœ):** (Total number of non-heterosexual people) / (Total people) = 100 / 200 = 0.50