However, the expedition did not have enough pen flares - devices which shoot flares up to 50 metres to frighten approaching bears - and only team leaders were equipped with them.
There were also a shortage of stakes for the tripwire, the device's trigger and tripwire itself - as well as mines to be situated around the perimeter of the camp site.
"We believed that the staff at BSES would do as they said and act responsibly to protect the children under their care," David Chapple told the hearing.
"We were never told the bear trip wires only sometimes work. The risk assessment refers to flares being available to all members of the expedition.
"If this had been implemented then Horatio would have at least had some time to defend himself other than with his bare hands."
Mr Chapple said a risk assessment suggested that a bear watch would take place at the camp, adding to the measures of pen flares, trip wires, training and a weapon to protect the group.
And a report by Sir David Steel published today said BSES should have had a bear watch at the time of the incident, to provide the group with advanced warning of the bear.
Dr Chapple said she was "more anxious" than her husband and son and went through every detail in the risk assessment to reassure herself about the group's protection.
"The trip was an expensive trip, I believed that they would have proper equipment," she said. "I thought Horatio would have a bear flare, I thought they would have things like bear spray.
"I believed that the camp would be protected by trip wire. I was naive, I had no idea how a camp side should be set up at that stage."
Richard Payne, chief leader of the expedition for BSES, said trip wires had first been used at camp sites in Svalbad on a previous summer expedition in 2010.
"My intention was that all young explorers and leader would have a pen flare," Mr Payne told the inquest.
"It was only when we landed at base camp, which is 40-50km from the airport, that I discovered there wasn't enough pen flares to equip everybody on the expedition.
"I took the decision that I would equip the leaders of each group and the doctors with pen flares."
Video: Polar bear cameras show life on ice
Mr Payne said he had changed the original trip wire from fishing line to a heavy duty braided fluorescent cord as the previous system was "going off too easily".
Equipment for the trip wire was put into a box along with four tonnes of equipment, which was loaded onto a vehicle and then a boat without being checked, he said.
When the box was unloaded the day before Horatio and the rest of the expedition arrived, equipment for the trip wire was found to be missing.
"There was a shortage of stakes on to which the trip wire mechanism is attached," he said. "There was a shortage of the small brass sear, which is a trigger for the device.
"There may have been some shortage of the trip wire itself."
Mr Payne said he met with base camp leaders to come up with a solution and decided to use a safety pin in the device to act as the trigger.
The camp sites were also changed to be triangular in formation to make up for a lack of mines, with Horatio's group having three mines instead of four situated around their site.
Assistant Coroner for Wiltshire and Swindon Ian Singleton asked: "Were you satisfied with the safety aspect of the trip as a whole?"
Mr Payne replied: "The three mines was the only downside, otherwise I was happy."
He added: "I have been camping in the Arctic for over 52 weeks and in all that time I haven't had a single polar bear encounter.
"I have never seen one and to have one in that area at that time of year and for it to behave as it did was totally out of character."
He said BSES had "completely revamped" its standard operations procedure for polar regions since the incident.
Mr Payne said he had since led three groups - separate from BSES - in Svalbad and made sure he was equipped with two rifles, two signal flares and pen flares for every member.
BSES have not conducted any expeditions in polar regions in the three years since Horatio's death, he added.
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- UK Independent
