SOLUTION: Please answer this question .., probability that a student A can solve a certain problem is 3/4 and that another student B can solve it is 4/5. If both try independently , what is

Algebra.Com
Question 1072401: Please answer this question .., probability that a student A can solve a certain problem is 3/4 and that another student B can solve it is 4/5. If both try independently , what is the probability that i) The problem is solved ? ii) The problem is not solved?
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
p(A) = 3/4

p(B) = 4/5

since these are independent events, .....

p(A and B) = p(A) * p(B) = 3/4 * 4/5 = 12/20 = 3/5.

p(A or B) = p(A) + p(B) - p(A and B)

p(A or B) is the probability that the problem is solved, since either A solves it or B solves it or both A and B solve it at the same time.

p(A or B) = p(A) + p(B) - p(A and B) becomes:

p(A or B) = 3/4 + 4/5 - 3/5.

put everything under the same common denominator and you get:

p(A or B) = 15/20 + 16/20 - 12/20

combine like terms under the same denominator and you get:

p(A or B) = (15 + 16 - 12) / 20

combine like terms to get:

p(A or B) = 19 / 20.

that's the probability that the problem will be solved.

the probability that the problem will not be solved is 1 - 19/20 = 1/20.

in the formula of p(A or B) = p(A) + p(B) - p(A and B), p(A and B) is assumed to be part of p(A) and part of p(B) which means they are being double counted.

the subtraction of p(A and B) therefore eliminates the double counting.


RELATED QUESTIONS

Please answer the following questions and explain how you derived each of your answer. (answered by stanbon)
Confused...Please Help! The probability that a student has a Visa card (event V) is... (answered by stanbon)
A multiple choise test has 3 questions, the first question has 3 possible answers a, b,... (answered by stanbon)
men: A students: 11 B students:15 C students: 6 D students: 1 women : A... (answered by ewatrrr)
I need help with my probability and statistics homework. Can someone please show me how... (answered by stanbon)
The probability that a student has a Visa card (event V) is .68. The probability that a... (answered by ikleyn)
Dear Tutor, please help me. 20 students take a test with three questions A,B and C.... (answered by Theo,ikleyn)
A student who has not studied for a multiple-choice test decides to guess the answers for (answered by math_helper)
I am so confused with this one, can someone please help? The table below shows the... (answered by ewatrrr)