flip a coin 3 times
a) what are the odds in favor of getting exactly 2 heads
b) what are the odds against getting at most 1 tail
i got a) 3/4 b) 7/8
i don't think they are right can someone help
If you flip a coin 3 times, here are the possible combinations:
HHH
THH
HTH
HHT
HTT
THT
TTH
TTT
Only 3 of the 8 possibilities will have exactly 2 heads.
The odds against getting at most 1 tail are the same as getting no tails. You are right with that answer.
I hope this helps. Thanks for asking.
To calculate the odds in favor of getting a specific outcome, we divide the number of ways the desired outcome can occur by the total number of possible outcomes.
Let's consider each question separately:
a) What are the odds in favor of getting exactly 2 heads?
To get exactly 2 heads, we can have HH, HT, or TH, where H represents a head and T represents a tail.
Total possible outcomes: Since flipping a coin 3 times gives us 2 options for each flip, the total number of possible outcomes is 2 * 2 * 2 = 8.
Desired outcomes: There are three possible combinations that result in exactly 2 heads: HH, HT, TH.
Therefore, the odds in favor of getting exactly 2 heads are 3/8.
b) What are the odds against getting at most 1 tail?
To get at most 1 tail means either getting no tails (0T) or getting only 1 tail (1T). Any other outcome would have more than 1 tail.
Total possible outcomes: 2 * 2 * 2 = 8 (as mentioned earlier).
Desired outcomes: There is only one outcome with no tails (0T), which is HHH. There are three outcomes with only 1 tail (1T): HHT, HTH, THH.
Therefore, the odds against getting at most 1 tail are 4/8, which simplifies to 1/2.
So, in summary:
a) The odds in favor of getting exactly 2 heads are 3/8.
b) The odds against getting at most 1 tail are 1/2.