Question

_{From a group of 50 people, 10 said they played cricket, 20 played tennis and 8 said they played both. If one member of the group was chosen at random, what is the probability that the person: (a) Plays cricket only (b) Plays neither cricket nor tennis (c) Plays cricket and tennis (d) Plays cricket or tennis}

Answer 1

Here, 10 said they played cricket, 20 played tennis and 8 said they played both.

Therefore , P(cricket) = 10/50 = 0.2

P(tennis) = 20/50 = 0.4

P(cricket and tennis) = 8/50 = 0.16

a) Probability that the person plays cricket only = P(cricket)

= 0.2

b) Probability that the person plays neither cricket nor tennis = 1 - P(the person plays cricket or tennis)

= 1 - (P(cricket) +  P(tennis) - P(cricket and tennis))

= 1 - (0.2 + 0.4 - 0.16)

=0.56

c) Probability that the person plays cricket and tennis =   P(cricket and tennis)

= 0.16

d) Probability that the person plays cricket or tennis = P(the person plays cricket or tennis)

= (P(cricket) +  P(tennis) - P(cricket and tennis))

= (0.2 + 0.4) - 0.16 = 0.44