The phrase "a much higher chance" is correct and usable in written English.
It can be used when comparing probabilities or likelihoods of different outcomes.
Example: "If we invest in marketing, we will have a much higher chance of reaching our target audience."
Alternatives: "a significantly greater likelihood" or "a considerably increased probability."
There is also a much higher chance of being ousted.
"We know that people marrying young have a much higher chance of divorcing," Dr. Stevenson says.
In the final analysis, if you look great, you'll feel great and if you feel great, there will be a much higher chance of you storming your interview.
Those girls have a much higher chance of suffering a fractured bone, especially if their soda of choice is cola, Harvard researchers say.
A tracking device may not stop the theft, but it gives a much higher chance of finding and retrieving the car".
By increasing the average number of products each customer has at Wells Fargo, the bank has a much higher chance of attaining the truly high-value ones.
John Cassidy, a tax investigations partner at the accountant PKF, says: "If something is wrong on your return, you've got a much higher chance of being spotted now.
"You're always friends, but there's a much higher chance for an argument when the Yankees are in first place and the Mets are going down the tank and vice versa.
"It is particularly endemic among young African American males, that in some communities in this country have a much higher chance of interacting with criminal justice than higher education.
Then a study indicated that, while babies who received steroids spent fewer days on mechanical ventilation and required less supplemental oxygen, which are clearly major benefits, they had a much higher chance of developing abnormalities in the brain.
"If your body is programmed to live off of very little food you have a much higher chance of getting diabetes with relatively small changes in lifestyle," he said.
