Chapter 10, Problem 10.1AYK

(a)

To determine

To find: the probability that the next 2 patients diagnosed with a spinal cord injury in Florida will be males.

Answer to Problem 10.1AYK

The probability that 2 consecutive patients with spinal cord injuries would be males is 0.5625.

Explanation of Solution

Given:

In the state of Florida, 75% of all patients who are first diagnosed with a spinal cord injury are males.

Calculation:

The probability that in the next two spinal cord injury events, both will be males can be calculated. To do this, it is assumed that the gender of the two consecutive events is unrelated and thus independent.

  $\begin{array}{l}p\left(male\right)p\left(male\right)={0.75}^2\hfill \\ p\left(male\right)p\left(male\right)=0.5625\hfill \end{array}$

Conclusion:

Therefore, the probability that 2 consecutive patients with spinal cord injuries would be males is 0.5625.

(b)

To determine

To find: the probability that at least 1 will be female and 1 will be male.

Answer to Problem 10.1AYK

The probability of at least one male is very likely with a probability of 0.9902 while the probability of at least one female is 0.7627.

Explanation of Solution

Calculation:

The probability that in the next 5 patients, one will be male can be determined as well as the probability that one will be female. To do this, the probability of 5 males or females needs to be calculated based on the probability of each individually. This is 0.75 for males and thus the remainder is the probability for woman, 0.25.

Probability of at least one male:

  $\begin{array}{l}p\left(atleastonemale\right)=p\left(not5females\right)\\ p\left(atleastonemale\right)=1-p\left(5females\right)\\ p\left(atleastonemale\right)=1-p\left({0.25}^5\right)\\ p\left(atleastonemale\right)=0.9902\end{array}$

Probability of at least one female:

  $\begin{array}{l}p\left(atleastonefemale\right)=p\left(not5males\right)\\ p\left(atleastonefemale\right)=1-p\left(5males\right)\\ p\left(atleastonefemale\right)=1-p\left({0.75}^5\right)\\ p\left(atleastonefemale\right)=0.7627\end{array}$

Conclusion:

Therefore,the probability of at least one male is very likely with a probability of 0.9902 while the probability of at least one female is 0.7627.