Over the past four years, two radiologist have made predictions, based on sonograms, on the sex of a baby. The following tables give their results. Rad. I Rad. II Predict M Predict F Predict M Predict F Baby is M 78 13 Baby is M 80 7 Baby is F 15 62 Baby is F 8 59 a) If a prediction by Radiologist I were chosen at random, what is the probability that the baby is male? b) If a prediction by Radiologist I were chosen at random, what is the probability thtat it is correct? c) If a prediction by Radiologist II were chosen at random, and the predictino is that the baby is female, how likely is she to be correct? d) If a prediction by radiologist I were chosen at random, and one by Radiologist II were also chosen at random, which is more likely to be incorrect? Justify your answer. e) For Radiologist II, are the events Predict M and Predict F indepnedent? Justify your answer.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Over the past four years, two radiologist have made predictions, based on sonograms, on the sex of a baby. The following tables give their results.
| Rad. I | Rad. II | |||||
| Predict M | Predict F | Predict M | Predict F | |||
| Baby is M | 78 | 13 | Baby is M | 80 | 7 | |
| Baby is F | 15 | 62 | Baby is F | 8 | 59 |
a) If a prediction by Radiologist I were chosen at random, what is the
b) If a prediction by Radiologist I were chosen at random, what is the probability thtat it is correct?
c) If a prediction by Radiologist II were chosen at random, and the predictino is that the baby is female, how likely is she to be correct?
d) If a prediction by radiologist I were chosen at random, and one by Radiologist II were also chosen at random, which is more likely to be incorrect? Justify your answer.
e) For Radiologist II, are the
Note: As per the guidelines, answers to 3 subparts have been provided.
Given information,
The probability table of Radiologist I is as follows:
| Predict M | Predict F | Total | |
| Baby is M | 78 | 13 | 91 |
| Baby is F | 15 | 62 | 77 |
| Total | 93 | 75 | 168 |
The probability table of Radiologist II is as follows:
| Predict M | Predict F | Total | |
| Baby is M | 80 | 7 | 87 |
| Baby is F | 8 | 59 | 67 |
| Total | 88 | 66 | 154 |
a)
From the probability table of Radiologist I,
Therefore, the required probability is 0.5417.
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