3. A student is taking two courses, history and math. The probability the student will pass the history course is 0.52, and the probability of passing the math course is 0.64. The probability of passing both is 0.42. (a) What is the probability of passing at least one? (b) What is the probability of passing neither? (c) What is the probability of passing either history or math but not both? (d) Are passing history and passing math independent events? Explain mathematically.
3. A student is taking two courses, history and math. The probability the student will pass the history course is 0.52, and the probability of passing the math course is 0.64. The probability of passing both is 0.42. (a) What is the probability of passing at least one? (b) What is the probability of passing neither? (c) What is the probability of passing either history or math but not both? (d) Are passing history and passing math independent events? Explain mathematically.
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Author:Amos Gilat
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Transcribed Image Text:3. A student is taking two courses, history and math. The probability the student will pass the
history course is 0.52, and the probability of passing the math course is 0.64. The probability
of passing both is 0.42.
(a) What is the probability of passing at least one?
(b) What is the probability of passing neither?
(c) What is the probability of passing either history or math but not both?
(d) Are passing history and passing math independent events? Explain mathematically.
Expert Solution
Step 1
Given ,
Let , A be the event that the student will pass history course
P( A ) = 0.52
B be the event that the student will pass math course
P( B ) = 0.64
The probability of passing both is 0.42
P( A and B ) = 0.42
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