A two-way table is given below, which shows the counts of the favorite leisure activities for...

A two-way table is given below, which shows the counts of the favorite leisure activities for 50 college students - 20 men and 30 women. Leisure Activity Yoga Sports TV Total Men 2 10 8 20 Women 16 6 8 30 Total 18 16 16 50 (a) What is the probability that a student selected at random is both a woman and student prefers Yoga? (b) What is the probability that a student is either a male or prefers sports? (c) What is the probability that a student selected at random prefers to watch television? (d) What is the probability that a female student selected at random, prefers television? (e) Draw the tree diagram for the above table. Be sure to label all probabilities.

Solutions

Expert Solution

activity	yoga	sports	tv	total
men	2	10	8	20
woman	16	6	8	30

a)Probability(woman and prefers yoga)=16/50=0.32

b)total men=20

total no. of students playing sports=16

no. of men playing sports=10

probability(either male or plays sports)= P(A)+P(B)-P(A and B)= 20/50+16/50-10/50= 0.52

c)total no. of students watching tv= 8+8=16

probability(students watching tv)= 16/50=0.32

d)Probability(female student watches tv)=8/30=0.27

e)each probability of the event occuring is in front of the arrow of the event

0.1

0.4 0.5

0.4

0.53

0.60.2

0.27

orchestra answered 1 year ago

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