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2. A traveler estimates that, for an upcoming trip, the probability of catching malaria is 0.18, the probability of catching typhoid is 0.13, and the probability of catching neither
of the two diseases is 0.75.
a. Draw a Venn diagram to represent this information.
b. Calculate the probability of catching both of the diseases.
c. Are the events "catches malaria" and "catches typhoid" independent? Explain your answer

Respuesta :

Answer:

a. Venn diagram is explained in the attached word file

b. 0.06

c. Not independent

Step-by-step explanation:

a. The attached word file explain the probabilities of catching malaria and typhoid using the Venn diagram

b. Probability of catching both diseases=P(M and T)=P(M∩T)=?

using the addition rule

P(MUT)=P(M)+P(T)-P(M∩T)

P(M)=0.18

P(T)=0.13

P(MUT)=P(M or T)=1-P(neither M nor T)=1-0.75=0.25

P(MUT)=P(M)+P(T)-P(M∩T)

0.25=0.18+0.13-P(M∩T)

P(M∩T)=0.18+0.13-0.25=0.06

c.  The two variables are independent if P(M∩T)=P(M)*P(T)

P(M∩T)=0.06

P(M)*P(T)=0.18*0.13=0.023

So, the events catching malaria and typhoid is dependent.

Ver imagen khansawaqar7

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