Question

probability question

Answer 1

\(\large \color{black}{\begin{align}
& \normalsize \text{Probability of solving specific problem independently by A and B are}\hspace{.33em}\\~\\
& \dfrac12\ \ \normalsize \text{and}\ \ \dfrac13\ \normalsize \text{respectively.}\hspace{.33em}\\~\\
& \normalsize \text{If both try to solve the problem independently, find the probability}\hspace{.33em}\\~\\
& \normalsize \text{ that exactly one of them solves the problem.}\hspace{.33em}\\~\\
\end{align}}\)

Answer 2

you want to find below two probabilities and then add them :

1) A solves the problem but B doesn't
2) A doesn't solve the problem but B solves it

Answer 3

P("A solves" AND "B doesnt solve") = ?

Answer 4

how did u know i need to find this

1) A solves the problem but B doesn't
2) A doesn't solve the problem but B solves it

Answer 5

good question, thats because of the phrase "exactly one of them"

Answer 6

"exactly one of them"

means


only one of them solves the problem

Answer 7

ok

Answer 8

P("A solves" AND "B doesnt solve") = P(A\(\cap\)B')

Answer 9

is this correct P("A solves" AND "B doesnt solve") = P(A∩B')

Answer 10

yes

Answer 11

Correct, it is easy, go ahead and find it...

Answer 12

P(A∩B')=P(A)-P(A∩B)

Answer 13

i suggest you not use the formulas to solve these problems,
use the problem to make sense of formulas instead

Answer 14

There are only four situations.
1. A solves it and B couldn't.
2. A couldn't solve it and B solves it.
3. A and B both solve it.
4. A and B both couldn't solve it (idiots!)

The question is asking for the probability of exactly one of them solves it (or one of them is an idiot!), so it is asking for the probability of 1 or 2 happening.

Answer 15

how can i solve it without formula "P(A∩B')"

Answer 16

you're given, probability that B solves the problem = 1/3
so can you guess the probability that B couldn't solve the problem ?

Answer 17

the probability that B couldn't solve the problem=2/3

Answer 18

I think it is true for all events X, P(X')=1-P(X).

Answer 19

Yes, since the events are independent, simply multiply the probabilities :

P("A solves" AND "B doesnt solve") = P("A solves")*P("B doesnt solve")
= ?

Answer 20

the probability that B couldn't solve the problem =1/2*2/3=1/3

Answer 21

Put it in another way, an event can either happen or not happen. No event can not happen and not not happen at the same time.

Answer 22

Correct. try finding the probability for other case too :

2) A doesn't solve the problem but B solves it

Answer 23

P("A doesnt solves" AND "B does solve") =1/6

Answer 24

Add them up and you're done!

Answer 25

=1/2

Answer 26

1/3 + 1/6 = 3/6

yeah 1/2 looks good to me

Answer 27

thnx