On the sinking of the Hood in 1941 Lutjens the German Admaral on Bismarck thought he was attcking the KGV and Hood not POW and he feared both Hood and KGV as both where the prides of the fleet and both fully worked up,
indeed if KGV had been with Hood not POW the Bismarck might have been sunk in the Denmark strait.
If you read up on it, the fact is that the Hood armor plating was far insupperior for WWII standards. You were right though Lutjens thought he was engaging the King George. The Prince of Whales that was with her was not fully operational and still had construction going on when it was diverted to intercept the Bismark. The Captains of the Hood & Prince of Whales made a vital mistake when it fired on the leadship the Prinz Eugen allowing the bismark to fire a rangeing salvo and destroy the hood with the second only 7 minutes into the engagement. The prince of Whales then suffered 4 hits from the bismark but not without inflicting the three shells that would require the bismark to head for port and thus sunk.
Timeline:
24 May 1941 (Saturday):
0543. Course 220?. Speed 28 knots. Bismarck and Prinz Eugen sight two ships at 17 miles on port side.
0552. Hood opens fire and the Battle of the Denmark Strait begins. Bismarck reports to Group North: "Am in a fight with two heavy units."
0555. Bismarck fires her first salvo at Hood followed shortly after by Prinz Eugen.
0555-0601. Bismarck is hit on the port side by three 35.6cm shells from Prince of Wales. One amidships under the armoured belt (section XIV), a second in her bows (section XXI), and the third one passes through a boat.
0601. Hood blows up and sinks in approximate position 63? 22' North, 32? 17' West.
0602-0609. Bismarck scores four hits on Prince of Wales.
0609. Fires last salvo at Prince of Wales. 93 x 38cm armour piercing shells (Psgr. L/4,4 (m.Hb)) fired. She is losing oil and her top speed is reduced to 28 knots. 2,000 tons of water in the forecastle.
0632. Bismarck reports to Group North: "Battlecruiser, probably Hood, sunk. Another battleship, King George or Renown, damaged. Two heavy cruisers keep up surveillance."
0705. Bismarck reports to Group North: "We have sunk a battleship at about 63? 10' North, 32? 00' West."
0801. Bismarck reports to Group North:
1. Loss of Electric plant No. 4.
2. Port Boiler Room No. 2 is taking water, but can be held. Water in forecastle.
3. Maximum speed 28 knots.
4. Denmark Strait 50 miles of floating mines. Enemy has radar instruments.
5. Intention: to put to St. Nazaire. No losses of personnel.
1200. Position 60? 50' North, 37? 50' West.
1240. New course 180?. Speed 24 knots.
1814. Turns 180? to starboard while the Prinz Eugen leaves the formation.
1840-1856. Fires some shells at Suffolk and Prince of Wales. No hits.
1914. Bismarck reports to Seekriegsleitung: ?Brief fight with King George without results. Prinz Eugen released for oiling. Opponent keeps up surveillance.?
2056. Bismarck reports to Group West and Seekriegsleitung: "Shaking off contacts impossible due to enemy radar. Due to fuel [shortage] will proceed directly to Saint-Nazaire."
2300. Sighted by the United States Coast Guard Cutter Modoc.
Midnight. Bismarck is attacked by eight Swordfish of the 825th Squadron (Lieutenant-Commander (A) Eugene Esmonde) from carrier Victorious. Bismarck's speed 27 knots. The battleship is hit by one 18 inch MK XII torpedo on the starboard side, amidships. The damage is insignificant, but the shock of the impact causes one casualty aboard: Oberbootsmann Kurt Kirchberg.