Pregunta
Two coins are tossed. Assume that each event is equally likely to occur.
a) Use the counting principle to determine the number of sample points in the sample space.
b) Construct a tree diagram and list the sample space.
c) Determine the probability that no tails are tossed.
d) Determine the probability that exactly one tail is tossed.
e) Determine the probability that two tails are tossed.
f) Determine the probability that at least one tail is tossed.
a) Use the counting principle to determine the number of sample points in the sample space.
b) Construct a tree diagram and list the sample space.
c) Determine the probability that no tails are tossed.
d) Determine the probability that exactly one tail is tossed.
e) Determine the probability that two tails are tossed.
f) Determine the probability that at least one tail is tossed.
Ask by Johnson Chang. in the United States
Mar 21,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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a) There are 4 possible outcomes when two coins are tossed.
b) The sample space is: {HH, HT, TH, TT}.
c) The probability of no tails is 1/4.
d) The probability of exactly one tail is 1/2.
e) The probability of two tails is 1/4.
f) The probability of at least one tail is 3/4.
Solución
a)
Each coin has 2 outcomes (Heads or Tails), so by the counting principle, the number of sample points is
Each coin has 2 outcomes (Heads or Tails), so by the counting principle, the number of sample points is
b)
We can construct a tree diagram as follows:
We can construct a tree diagram as follows:
-
First coin toss:
- Heads (H)
- Tails (T) -
Second coin toss for each branch:
- If first toss is H: second toss can be H or T → outcomes: HH, HT.
- If first toss is T: second toss can be H or T → outcomes: TH, TT.
Thus, the sample space is:
c)
No tails tossed means both coins show Heads. There is 1 favorable outcome (HH) out of 4. Therefore, the probability is
No tails tossed means both coins show Heads. There is 1 favorable outcome (HH) out of 4. Therefore, the probability is
d)
Exactly one tail tossed corresponds to the outcomes HT and TH. There are 2 favorable outcomes. Thus, the probability is
Exactly one tail tossed corresponds to the outcomes HT and TH. There are 2 favorable outcomes. Thus, the probability is
e)
Two tails tossed corresponds to the outcome TT only. There is 1 favorable outcome. Thus, the probability is
Two tails tossed corresponds to the outcome TT only. There is 1 favorable outcome. Thus, the probability is
f)
At least one tail tossed means we include outcomes with one tail or two tails: HT, TH, TT. There are 3 favorable outcomes. Thus, the probability is
At least one tail tossed means we include outcomes with one tail or two tails: HT, TH, TT. There are 3 favorable outcomes. Thus, the probability is
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Simplifique esta solución The Deep Dive
a) Using the counting principle, each coin has 2 possible outcomes: Heads (H) or Tails (T). When tossing two coins, you multiply the number of outcomes for each coin: 2 (for the first coin) × 2 (for the second coin) = 4 sample points in the sample space.
b) The tree diagram for tossing two coins looks like this:
- For Coin 1:
- H
- Coin 2: H
- Coin 2: T
- T
- Coin 2: H
- Coin 2: T
- H
This leads to the sample space: {HH, HT, TH, TT}.
c) The probability of getting no tails (i.e., getting HH) is calculated by the formula: P(no tails) = Number of favorable outcomes / Total outcomes = 1/4, since there’s only 1 way to get no tails out of the 4 possible outcomes.
d) To find the probability of getting exactly one tail (HT or TH), we count the favorable outcomes. There are 2 outcomes (HT and TH) that result in exactly one tail. Thus, P(exactly one tail) = Number of favorable outcomes / Total outcomes = 2/4 = 1/2.
e) The probability of tossing two tails (TT) is straightforward. There is only 1 favorable outcome (TT) out of 4 possible outcomes. Therefore, P(two tails) = 1/4.
f) To determine the probability of getting at least one tail, we can find this by subtracting the probability of getting no tails from 1. So, P(at least one tail) = 1 - P(no tails) = 1 - 1/4 = 3/4. In terms of outcomes, this includes HT, TH, and TT.
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