After all the market fuss that went on last week and early this week, Brexit mightn’t happen after all.

As is being reported by The Australian Financial Review, Hamish Douglass, chief executive at Magellan Financial Group, estimates there is a 25% chance that Britain will decide against leaving the European Union despite the 51.9% to 48.1% vote in favour of doing so on Friday last week.

Markets around the world were widely expecting the Remain campaign to win on the day and, when it didn’t, it triggered a major sell-off in equities. Australia’s S&P/ASX 200 (Index: ^AXJO) (ASX: XJO) has retreated in the time since, with a number of companies such as Henderson Group plc (ASX: HGG) and Clydesdale Bank plc (ASX: CYB) experiencing far more violent sell-offs.

But markets have showed signs of rebounding in some sessions since then, which is possibly at least partially based on the market’s hopes that Brexit won’t actually happen. After all, the referendum was not binding and many Leave voters have expressed their regret in doing so in the time since.

Millions of individuals have also signed an online petition, arguing that there should be a second referendum vote when “the remain or leave vote is less than 60% based on a turnout less than 75%“.

Brexit probably will still happen

Before I go any further and get readers’ hopes up, the likelihood is that Brexit will still go ahead. Britain’s Prime Minister David Cameron, who announced his resignation after the Leave party won the vote, has already stated that the wishes of the people (as represented by the referendum results) must be honoured.

Considering the heavy backlash the country has received since the result was finalised, it seems the most likely situation from here would be that the UK leaves the EU, but negotiates to keep access to Europe’s single market to soften the economic blow.

If it were to do this, it would have to contribute to the EU budget and allow free movement of labour within Europe, which would defy one of the major reasons for them wanting to leave in the first place.

Nonetheless, many individuals would likely agree to this after realising just how severely leaving the EU could impact their economy. Douglass gives this scenario a 50% chance.

Gideon Rachman from Financial Times also weighed in on the immigration debate, suggesting that if the UK were allowed to limit the number of EU nationals moving to Britain it could result in a Remain win were a second referendum vote to be held.

He said (my emphasis): “Even so, with 48 per cent of voters opting to stay in the union, the result was extremely close. If the Remain campaign could fight a second referendum with a proper answer to the question of immigration it should be able to win fairly easily.”

Whether or not the EU would actually give Britain such a concession is another thing. After all, it won’t want to give the impression that Britain has it over a barrel which could lead other EU members to demand better terms as well.

The other scenario is if Britain were to choose to exit and demand total sovereignty, which Mr Douglass estimates is a 25% chance of happening.

What should investors do?

As if the drama of Brexit wasn’t enough to send the market into a frenzy, the possibility that Brexit may not even happen creates more uncertainty that investors must contend with.

Although the ASX 200 rose on Monday and then again on Wednesday, it’s fair to assume that the volatility is not over and that investors will (justifiably) continue to invest cautiously.

However, what should be noted is the number of shares that were sold off late last week and early this week, even when the businesses those shares represent wouldn’t necessarily be impacted even if Britain does follow through with its divorce from the EU.

Investors were seen piling back into certain shares again yesterday, including automotive aftermarket parts business Burson Group Ltd (ASX: BAP) whose share price hit a new all-time high of $5.67. Shares of other quality businesses such as CSL Limited (ASX: CSL) and Blackmores Limited (ASX: BKL) marched higher as well.

For now, investors are right to tread cautiously and consider the potential implications of investing in businesses that are directly exposed to Europe. However, it’s also a great time to be on the lookout for shares of quality businesses that have been sold down heavily, as it could be a great buying opportunity as well.

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Motley Fool contributor Ryan Newman owns shares of Burson. The Motley Fool Australia owns shares of Burson. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy. This article contains general investment advice only (under AFSL 400691). Authorised by Bruce Jackson.