In General, One Woman In Ten Will Develop Breast Cancer Rese

In General One Woman In Ten Will Develop Breast Cancer Research Has S

In general, one woman in ten will develop breast cancer. Research has shown that one woman in 650 carries a mutation of the BRCA gene. Nine out of ten women with this mutation develop breast cancer. The problem asks for the probability that a randomly selected woman will carry the gene mutation and develop breast cancer.

Paper For Above instruction

The probability that a randomly selected woman will carry the BRCA gene mutation and develop breast cancer can be calculated using the principles of probability theory, specifically the multiplication rule for dependent events. To determine this, we need to analyze two probabilities: the probability that a woman carries the BRCA mutation and the probability that a woman with this mutation develops breast cancer. Combining these provides the joint probability of both events occurring simultaneously.

Firstly, the probability that a woman carries the BRCA gene mutation, denoted as P(Mutation), is given as 1 in 650, which can be expressed as a decimal:

P(Mutation) = 1/650 ≈ 0.001538

Secondly, the probability that a woman with the mutation develops breast cancer, denoted as P(Cancer | Mutation), is 9 out of 10:

P(Cancer | Mutation) = 0.9

The overall probability that a randomly selected woman both carries the mutation and develops breast cancer, denoted as P(Mutation and Cancer), is the product of these two probabilities:

P(Mutation and Cancer) = P(Mutation) × P(Cancer | Mutation)

Plugging in the values:

P(Mutation and Cancer) ≈ 0.001538 × 0.9 ≈ 0.001384

Expressed as a percentage, this is approximately 0.1384%.

This indicates that about 0.1384% of women are expected to both carry the BRCA mutation and develop breast cancer. It is important to interpret this probability within the context of the broader population. Although the chance for any individual woman is relatively low, the impact on public health remains significant given the severity of breast cancer.

Moreover, understanding the joint probability emphasizes the importance of genetic screening and targeted interventions. Women identified as carriers through genetic testing can benefit from increased surveillance and preventive measures, potentially reducing the incidence of breast cancer among high-risk groups.

In conclusion, based on the given data, the probability that a randomly selected woman will carry the BRCA gene mutation and develop breast cancer is approximately 0.001384, or 0.1384%. This calculation underscores the significance of genetic factors in breast cancer risk assessment and highlights the value of genetic counseling and testing for women with familial history or other risk factors.

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