have equal probabilities?
A. 4H and 1H B. 2H and 0H C. 3H and 1H D. 3H and 3H
5 answers
D. 3H and 3H. If both coins are fair, then each coin has a 50% chance of landing heads up and a 50% chance of landing tails up. This means that for any combination of coin tosses, there is an equal probability of getting that combination. In the case of 3H and 3H, there are 8 possible outcomes: HHHHHH, HHHTTT, HHTHTH, HTHHTH, HTHTHT, THHHTH, THHTHH, THTHTH. Since there is only one outcome that has 3H and 3H, the probability of getting that outcome is 1/8, or 12.5%, which is equal to the probability of getting any other outcome.
how about 3H and 1H? - they have equal probability
If both coins are fair, then there are four possible outcomes when tossing two coins: HH, HT, TH, and TT. Each of these outcomes has an equal probability of 1/4 or 25%. Among these four outcomes, 3H and 1H can occur in three of them: HHT, HTH, and THH.
So the probability of getting 3H and 1H is 3/4 x 1/2 x 1/2 = 3/16 or 18.75%. This is exactly the same probability of getting 1H and 3T, which is another possible outcome that also occurs in three out of the four possible outcomes.
Therefore, 3H and 1H do have an equal probability to occur, just like other combinations such as 1H and 1T or 2H and 0H.
So the probability of getting 3H and 1H is 3/4 x 1/2 x 1/2 = 3/16 or 18.75%. This is exactly the same probability of getting 1H and 3T, which is another possible outcome that also occurs in three out of the four possible outcomes.
Therefore, 3H and 1H do have an equal probability to occur, just like other combinations such as 1H and 1T or 2H and 0H.
how about A. 4H and 1H B. 2H and 0H
A. 4H and 1H:
If you toss two fair coins five times, there are 32 possible outcomes. Among these outcomes, there is only one where you get 4 heads and 1 tail: HHHHT. Therefore, the probability of getting 4 heads and 1 tail is 1/32 or 3.125%.
B. 2H and 0H:
If you toss two fair coins two times, there are 4 possible outcomes: HH, HT, TH, TT. Among these outcomes, there is only one where you get 2 heads and 0 tails: HH. Therefore, the probability of getting 2 heads and 0 tails is 1/4 or 25%.
If you toss two fair coins five times, there are 32 possible outcomes. Among these outcomes, there is only one where you get 4 heads and 1 tail: HHHHT. Therefore, the probability of getting 4 heads and 1 tail is 1/32 or 3.125%.
B. 2H and 0H:
If you toss two fair coins two times, there are 4 possible outcomes: HH, HT, TH, TT. Among these outcomes, there is only one where you get 2 heads and 0 tails: HH. Therefore, the probability of getting 2 heads and 0 tails is 1/4 or 25%.
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