Answer :
Part A)
Probability you both have cancer and test indicates you have cancer is:
.04*.99
Probability test indicates you have cancer. You have to look at 2 cases:
The one above and the one where you do not have cancer but test says you do. ---> .01*.96
The total probability then is the sum of the 2 cases:
.04*.99 + .01*.96
Finally, the conditional probability is first case divided by total probability:
(.04*.99)/(.04*.99 + .01*.96)
Part B)
Same as part a, except we are looking at when test says you do Not have cancer. If you have cancer, this occurs 1% of the time. If you dont, then 99%.
The probabilities are flipped.
The conditional probability is:
(.04*.01)/(.04*.01 + .99*.96)
Probability you both have cancer and test indicates you have cancer is:
.04*.99
Probability test indicates you have cancer. You have to look at 2 cases:
The one above and the one where you do not have cancer but test says you do. ---> .01*.96
The total probability then is the sum of the 2 cases:
.04*.99 + .01*.96
Finally, the conditional probability is first case divided by total probability:
(.04*.99)/(.04*.99 + .01*.96)
Part B)
Same as part a, except we are looking at when test says you do Not have cancer. If you have cancer, this occurs 1% of the time. If you dont, then 99%.
The probabilities are flipped.
The conditional probability is:
(.04*.01)/(.04*.01 + .99*.96)