Hi,
DozyWannabee
The thought of two or more failing was thought to be exceptionally remote
be exceptionally remote 
A short one ...
Put 3 fingers in water .. they will be all wet
Thales AA pitot probes in foul weather conditions with the voting logic of the FCU and FMC didn't raise its head until a decade later, and they've been trying to fix it since.
Airbus. December 1995 TFU 34.13.00.005: « STRONG CUMULO-NIMBUS (Cb) CONTAINING A HIGH DENSITY OF ICE CRYSTALS CAN BEEN ENCOUNTERED, PARTICULARLY IN THE INTERTROPICAL CONVERGENCE ZONE (ITCZ). IN SUCH AN ICY AND TURBULENT ATMOSPHERE, THE A/C AIR DATA PARAMETERS (PRESSURE DEPENDANT) MAY BE SEVERELY DEGRADED, EVEN THOUGH THE PROBE HEATERS WORK PROPERLY. IT HAS APPEARED THAT THE CHARACTERISTICS OF SUCH AN ENVIRONMENT COULD EXCEED THE WEATHER SPECIFICATIONS FOR WHICH THE PITOT PROBES ARE CURRENTLY CERTIFIED. »
January 1999. Report BFU accident 5X002-0/98 : « The specification for the pitot tubes should be changed so as to allow unrestricted flight operations in heavy rain and under severe icing conditions. The installation of the improved pitot tubes already designed should subsequently be prescribed for all types concerned by the SIL no. 34-0147 (A 320, A 321, A 330, A 340). »