Bart is taking two classes, backpacking and biology. His probability of passing backpacking is 0.54, that of failing biology is 0.83, and that of passing at least one of the two courses is 0.65. Find the probability of the following.
A. Joe will pass both courses.
B. Joe will pass exactly one course.
C. Joe passes neither course.
You have the probability of passing each course, and the probablity of passing at least one. Using joint probability, find A and B.
For C, wouldnt passing neither course be the probability of failing 1, then multiplied by the prob of failing the other?
To find the probabilities A, B, and C, we will use the concept of joint probability and the complement rule.
A. Joe will pass both courses.
To find the probability of passing both courses (backpacking and biology), we multiply the probability of passing backpacking (0.54) by the probability of failing biology (0.83), since these events are independent.
P(A) = P(passing backpacking) * P(failing biology)
P(A) = 0.54 * 0.83 = 0.4482
B. Joe will pass exactly one course.
To find the probability of passing exactly one course (either backpacking or biology), we need to calculate the probability of passing both courses and subtract it from the probability of passing at least one course.
P(B) = P(passing at least one course) - P(passing both courses)
P(B) = 0.65 - 0.4482
P(B) = 0.2018
C. Joe passes neither course.
To find the probability of failing both courses (neither backpacking nor biology), we can use the complement rule. The complement of passing at least one course is failing both courses.
P(C) = 1 - P(passing at least one course)
P(C) = 1 - 0.65
P(C) = 0.35
Therefore,
A. The probability of Joe passing both courses is 0.4482.
B. The probability of Joe passing exactly one course is 0.2018.
C. The probability of Joe passing neither course is 0.35.