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% considered th

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Question 1191591: 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) ๐‘ƒ(๐ป^c)



Answer by CPhill(1959)   (Show Source): You can put this solution on YOUR website!
Here's how to calculate those probabilities:
1. **Calculate the number of people in each category:**
* **Males (M):** 120
* **Non-males (Mแถœ):** 200 - 120 = 80
* **Heterosexual males (M โˆฉ H):** 120 * 0.60 = 72
* **Non-heterosexual males (M โˆฉ Hแถœ):** 120 - 72 = 48
* **Heterosexual non-males (Mแถœ โˆฉ H):** 80 * 0.35 = 28
* **Non-heterosexual non-males (Mแถœ โˆฉ Hแถœ):** 80 - 28 = 52
* **Total heterosexual (H):** 72 + 28 = 100
* **Total non-heterosexual (Hแถœ):** 48 + 52 = 100
2. **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
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