Answer to Question #127227 in Statistics and Probability for zeleke

Question

The probability that Martha will play soccer is 0.3, the probability that Ayyantu will play soccer is 0.4, and they make their decisions independently.

6. The probability that both of them will play soccer is

7. The probability that Martha or Ayyantu or both will play soccer is

8. The probability that both Martha and Ayyantu will not play soccer is

Answer 1

Let M = event that Martha will play soccer.

Let A = event that Ayyantu will play soccer.

P(M) = 0.3

and P(A) = 0.4

a.

P( M and A ) = P(M)*P(A) , since they are independent events

= 0.3*0.4 = 0.12

b.

P(M or A) = P(M) + P(A) - P(M and A)

Hence P(M or A)= 0.3+0.4-0.12= 0.58

c.

P(both will not play)= P(M will not play)P(A will not play)

=(1-0.3)(1-0.4)

=0.7*0.6

=0.42