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We all hope we will be part of the lucky few. It's why loads of people play the lottery, not minding the odds.

Optimism is a human impulse. When we're sick, diagnosed with something sinister, we tend to accept the option of medical treatment even when told that only 10 per cent of patients ever benefit. The culture compels us to believe in medical science, its wonders and miracles. We hope there's a Dr. House somewhere who can figure things out and fix us.

There's that. That's us. But step aside from the rote behaviour and here's a vital question: If you knew you were dying, what would you do with the time you had left?

It's complicated, isn't it? As we know from reaction to the recent Supreme Court decision on assisted suicide, the term "sanctity of life" has different meaning for different people.

Life, its value and meaning, especially when there is only a short time left, provokes feelings and reactions that have profound emotional heft.

Frontline: Being Mortal (PBS, Tuesday, 10 p.m.), based on the bestselling book by surgeon Atul Gawande, tackles with fierce insight and poignancy the way in which the medical profession treats those who are dying and how, often, it fails to give them the best options. It's truly excellent TV.

The force of Gawande's book is rooted in personal and professional experience. He says, early on in the program, that it's all about "having a discussion that begins to say, 'Look, you only have a few months to live. What do we do to make the best of your time?' No one's ready to have that conversation. Least of all me."

A case that troubles him with heart-scalding anguish, and which he discusses at length, is that of 34-year-old Sarah, who was pregnant when she was diagnosed with late-stage cancer. She discussed the possibility of not dying in hospital, of wanting a little time with her child. Gawande's course of action, though, was to try another and then another course of treatment. Four different kinds of chemotherapy, brain radiation. She was scheduled for an experimental therapy to start on a Monday and she died on the Saturday before.

Gawande realized that he had never had a meaningful discussion with her and her family about what she truly wanted from her last weeks and months. The patient was trapped inside a system that kept doing what it does. Now he sees that as a failure. And it haunts him.

And then there is the matter of his own father. Also a doctor and in his 70s, he was still active when diagnosed with a slow-growing brain tumour. Gawande had conversations with his dad that were son-to-father, not doctor-to-doctor. That changed his perspective and gave him a new grasp of what the aims and goals of a patient might be, as opposed to the aims of a doctor treating a patient. He says that his father "wanted to be social." And eventually his father said, "Let me die."

There are weighty and difficult issues at the heart of everything Gawande touches upon. In the context of an aging population and a stressed medical system, they must be faced. This Frontline will make you think about life, death and dying in a manner that requires us to step away from the idea of being part of the lucky few who benefit from medicine when the odds are slim, and being part of the lucky few who have a choice over how we die.

Also airing Tuesday

Fresh Off the Boat (ABC, 8 p.m.) is worth your time for a good laugh. It's early days but some critics are calling it "the best new comedy of 2015." Based on restaurateur Eddie Huang's memoir – which is a very good book – it's lively, goofy and touches on issues of race and class with deft hilarity. The Huang family has moved from Washington to Orlando so that dad Louis (Randall Park) can open a steak restaurant. It's one version of the American Dream. His sons have other versions – girls, popularity, sports and fun. The gentle mockery of white suburban life is sweet, the trial and tribulations of the Huang boys is presented as a finely comic cautionary tale.

All times ET. Check local listings.