There are a total of 10 buttons in the bag.
The probability of picking a yellow button, P(Y) is:
5/10 or 1/2
The probability of picking a green button, P(G) is:
2/10 or 1/5
The probability of picking a red button, P(R) is:
3/10
QUESTION A:
Probability of yellow (Y) or red (R) button:
P(Y or R) = P(Y) + P(R)
= 5/10 + 3/10
= 8/10
= 4/5
In questions that ask P(A) or P(B), the word 'or' means you add them together.
QUESTION B:
Probability of green (G), replaced, then red (R) button:
P(G and R) = P(G) × P(R)
= 2/10 × 3/10
= 6/100
= 3/50
In question that ask P(A) and P(B), the word 'and' means you multiply them together.
Also, if the first picked object is replaced, then the total number of objects remain the same - which means that the probabilities of the next pick doesn't change. So, event B (the event of picking the B object) is not dependent (or independent) of event A. In other words, event A does not affect the outcome of even B.
QUESTION C:
Probability of red (R), kept, then yellow (Y) button:
P(R and Y) = P(R) × P(Y)
= 3/10 × 5/9
= 15/90
= 1/6
Notice that because the red button was kept, the total number of buttons was reduced to 9. This changes the probability of picking a yellow and thus affects the overall probability of picking a red button, then a yellow.
In cases like these, event B is dependent on event A, meaning that event A has an impact on event B.
