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Of a group of 500 people, 60 are fit enough to climb Mount Shasta in California. The group has 300 women and 200 men. 12% of the men are fit to climb the mountain. What is the probability that a person picked at random from the group is a male or is fit to climb Mount Shasta?

Respuesta :

meerkat18
The number of male in the group is a total of 200 mem. The number that is fit to climb in Mount Sasha is 12%  of the men or 0.12*200 equal to 24. Hence the  probability that a person picked at random from the group is a male or is fit to climb Mount Shasta is (200/500) + (24/500) equal to 44.8 percent
frika

1. Count how many men are fit to climb:

200 men - 100%

x men - 12 %

Then

[tex] \dfrac{200}{x}=\dfrac{100}{12} ,\\ \\ x=\dfrac{200\cdot 12}{100}=24. [/tex]

2. 60 are fit enough to climb Mount Shasta in California, among them 24 are men, then 60-24=36 are women.

3. The probability that a person picked at random from the group is a male is [tex] Pr(\text{male})=\dfrac{200}{500}=0.4. [/tex]

4. The probability that a person picked at random from the group is fit to climb Mount Shasta is

[tex] Pr(\text{fit to climb})=\dfrac{60}{500}=0.12. [/tex]

5. Use formula

[tex] Pr(\text{male or fit to climb})=Pr(\text{male})+Pr(\text{fit to climb})-Pr(\text{male and fit to climb}). [/tex]

6.

[tex] Pr(\text{male and fit to climb})=\dfrac{24}{500}=0.048. [/tex]

Then

7.

[tex] Pr(\text{male or fit to climb})=0.4+0.12-0.048, [/tex]

[tex]Pr( \text{ male or fit to climb })=0.472. [/tex]

Answer: 0.472 (or in percent near 47.2%).