Answer to Question #126975 in Statistics and Probability for mengesha

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

Solution:

Let A be the event that Martha will play soccer.

Let B be the event that Ayyantu will play soccer.

Then P(A)=0.3, P(B)=0.4.

6.Since these events are independent, then P(AB)=P(A)P(B)=0.3$\cdot$0.4=0.12

7.P(A+B)=P(A)+P(B)-P(AB)=0.4+0.3-0.12=0.58

8.P( $\overline{A}$ $\overline{B} )=P(\overline{A} )P(\overline{B})$

$P(\overline{A} )=1-P(A)$ =1-0.3=0.7

$P(\overline{B} )=1-P(B)$ =1-0.4=0.6

$P(\overline{A}$ $\overline{B} )=0.7\cdot0.6=0.42$