Then verify by drawing the sample space and calculating the

Question

Three coins are fairly tossed.

E_l: first two coins are heads;

E₂: last coin is a head;

E₃: all three coins are heads.

Try to answer the following questions intuitively (does knowledge of the condition affect your betting odds?). Then verify by drawing the sample space and calculating the relevant probabilities for (3-24).

(a) Are E_l and E₂ independent?

(b) Are E₂ and E₃ independent?