The contingency table below provides a joint frequency distribution for a random sample of patients at a hospital classified by blood type and sex. Blood Type $1771593915390\begin{array} { | l | c | c | c | c | c | } \hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { AB } & \text { Total } \\\hline \text { F } & 105 & 85 & 24 & 11 & 225 \\\hline M & 72 & 74 & 15 & 4 & 165 \\\hline \text { Total } & 177 & 159 & 39 & 15 & 390 \\\hline\end{array}$ If a person is selected at random from the sample,find the probability that the person has blood type A or is female.

A) 0.985
B) 0.767
C) 0.378
D) 0.535
E) 0.218

Question

The contingency table below provides a joint frequency distribution for a random sample of patients at a hospital classified by blood type and sex. Blood Type

1771593915390\begin{array} { | l | c | c | c | c | c | } \hline \text { Sex } & \text { O } & \text { A } & \text { B } & \text { AB } & \text { Total } \\\hline \text { F } & 105 & 85 & 24 & 11 & 225 \\\hline M & 72 & 74 & 15 & 4 & 165 \\\hline \text { Total } & 177 & 159 & 39 & 15 & 390 \\\hline\end{array}

If a person is selected at random from the sample,find the probability that the person has blood type A or is female.

A) 0.985
B) 0.767
C) 0.378
D) 0.535
E) 0.218

Precious Gastin · Accepted Answer

Final Answer : B, Explanation :  To find the probability that the person has blood type A or is female, we add the probability of being female to the probability of having blood type A, and subtract the probability of being both female and having blood type A to avoid double counting. Probability of being female = 225/390. Probability of having blood type A = 159/390. Probability of being female and having blood type A = 85/390. Thus, the total probability = (225 + 159 - 85) / 390 = 299 / 390 = 0.767.

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