sarcastic__atom
Tabatha decorates the walls of her room by pasting 80 balloons, which include 20 red balloons. She randomly selects one balloon at a time and then pastes it on the wall. What is the probability that the third balloon she selects is a red balloon?
(A) 1/80
(B) 1/20
(C) 1/4
(D) 1/2
(E) None of the above
If she selects and paste it on the wall then how come the probability still remains 1/4 it should be 19/79 right ?
The point is that we don't know what the first two balloons colors were, so without that information, nothing changes when calculating the probability for the third balloon.
Consider this: there are 8 cards, 5 spades, and 3 hearts. What is the probability that the first card you pick will be a spade? Clearly, it’s 5/8.
Now, suppose I randomly remove three cards without telling you which cards were thrown away. What is the probability now that you pick a spade out of the 5 remaining cards? Even though the sample has been reduced, the probability still remains 5/8. Why should it change?
Another scenario: using the same 8 cards (5 spades and 3 hearts), imagine you are allowed to pick one card, but only from a randomly selected subset of 5 cards. What is the probability of picking a spade? Again, it remains 5/8.
In all these cases, the probability does not change. If it were to increase or decrease, it would imply that the probability of picking a heart would inversely change. But there is no reason for this to happen, as the process remains random, and we lack information about the removed or previously picked cards.
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