Answer to Question #216173 in Statistics and Probability for qianhe

Question

 The probability that it will be sunny tomorrow is 1/3. If it is sunny, the probability that Ali plays badminton is 4/5. If it is not sunny, the probability that Ali plays badminton is 2/5.

a)        Draw a tree diagram to describe about the whole situation                                           

b)        Find the probability that Ali plays badminton tomorrow          

Answer 1

a)

b)

$$P(B)=P(B|Sun)P(Sun)+P(B|\overline{Sun})P(\overline{Sun})$$

$$=\dfrac{4}{5}(\dfrac{1}{3})+\dfrac{2}{5}(\dfrac{2}{3})=\dfrac{8}{15}$$

The probability that Ali plays badminton tomorrow is $\dfrac{8}{15} .$