Question

Five fair coins will be flipped; each coin is a different color. You may not use a calculator, but you may also leave your answer as a sum, product, and/or quotient of integers. You do not need to simplify. The events E, F, and G are defined as follows: E: There are an even number heads, F: The total number of heads is > 4, G: All five coins come up heads, H: The first coin comes up heads. Answer each question in the space provided below, you do not need to justify your answers. 1. Calculate p(E). 2. Calculate p(F). 3. Calculate p(G). 4. Calculate p(H). 5. What is p(E|H)? 6. What is p(F|H)? 7. What is p(E|F)? 8. What is p(G|H)? 9. Which pairs of events among E, F, and H are independent? (Note that G is not present in the list) 10. Are G and H independent?

Answer 1

Here be Then total Bi is detined heads out of tive Coins Hipped number of sample space, n):95-32 alow consider 13, B1 B2 B3 B4 , By events where event of getting exactly i Cindependent and tail) coin tossed Then observing that there are exactly sei ors drows Containing i heads . as the J Sequence (1) ..n CE = n CB, J V B₂ VB4) Seot Seat 5e4 [- al are pndependen 1 + 10 +3 :. PE) 16 NE) nos 32 (2) n(F) c ::. DE n (B4 vBs ) = 544 +Ses =57126 = 3/10 ne) nos) - 6 32 3) nCG) = nCBs) ses al - PCG) = ng) ㅗ nes) 32 n CH) Yeo + 46, +4e₂t4e3+ 4e4 = 16 PH) пH nes) 16 = 1 / 4 - PENH ne PH) Again (Enho 4e, tuez (5) How PCE/H) 32 ПН ACH) - 4+4 = 8

..PE/H) =8 = 1/2 16 6) (Enh) Cez t4e4 = 4+1 -5 PCFH = n CFNH nch) 5 T6 7) nCEnF) = Sey = 5 PELE) n cenf) -5 nce) 8 = 1 n CGNH) - P CG/H) = n(GOH) ñ CH) 16 a E and G are endependent 10) No, G and H are not independent