A big (cancerous) coincidence?

The immediate thing playing on my mind is the question of whether my test result was negative for a BRCA1 or BRCA2 mutation because
a)      There was a BRCA1 or BRCA2 mutation in my family and I didn’t inherit it.
b)      The breast and ovarian cancers in my family have been caused by either an alteration in another gene (or genes) or something is affecting the BRCA1 or BRCA2 genes from a distance.
These were the two possibilities raised by the Genetics Clinic but I want to also consider a third:
c)       The breast and ovarian cancers in my family were not caused by anything genetic and it’s just an unfortunate coincidence.

I want to tackle the third possibility first – that the cancers in my family are sporadic, and genes have never played a role.

On my mother’s side of the family, in the 3 generations above me, there is only one woman per generation (alive or dead). My mother, her mother, her mother. So what are the chances of 2 of them getting breast cancer and one of them getting ovarian cancer purely by chance?

Ovarian cancer

According to Macmillan about 1 in every 50 (2% of) women in the UK develops ovarian cancer during her lifetime.
According to the American Cancer Society a woman's risk of getting ovarian cancer during her lifetime is about 1 in 72.

My family are from the UK so I will use the 1 in 50 figure.

Breast cancer

For the breast cancers I am going to take age of diagnosis in to account because this does affect risk (and unlike with ovarian cancer I found these figures broken down by age readily available). There are different figures given by different organisations. I will give two examples

According to Breast Cancer Care these are the estimated risks of a woman in the UK developing breast cancer according to age:
Risk up to age 29, 1 in 2,000.
Risk up to age 39, 1 in 215.
Risk up to age 49, 1 in 50. (My mom was 47 at diagnosis)
Risk up to age 59, 1 in 22. (My grandmother was 59 at diagnosis)
Risk up to age 69, 1 in 13.
Lifetime risk, 1 in 8.

According to Breastcancer.org these are the estimated risks of a woman in the United States developing breast cancer according to age:
From age 30 to 39, 1 in 227.
From age 40 to 49, 1 in 68.
From age 50 to 59, 1 in 42.
From age 60 to 69, 1 in 28.
Lifetime risk, 1 in 8.

Again, as my family are in the UK I will go with the 1 in 50 and 1 in 22 figures.

My calculation

What are the chances of the only three women across three generations of a family developing one ovarian cancer, one breast cancer age 47 and one breast cancer age 59? I’m not a mathematician so if you think I have miscalculated this, please let me know in the comments!

1/50 x 1/50 x 1/22 = 1/55,000
Or a 0.000018% chance.

It is possible that it was pure coincidence that my mother, her mother, and her mother all had breast or ovarian cancer. On a planet with over 7 billion people this is bound to happen somewhere. But to give this some more context: according to the National Cancer Institute BRCA1 and BRCA2 mutations account for about about 5 to 10 percent of all breast cancers and around 15 percent of ovarian cancers overall. It’s much more likely that the cancers in my family are hereditary than not and that’s important to me when considering my own future risk, so I’m not going to spend any more time mulling over option C above!

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