Three coins are tossed, and the number of heads observed is recorded. (Give your answers as fractions.)
(a) Find the probability for 0 heads.
(b) Find the probability for 1 head.
(c) Find the probability for 2 heads.
(d) Find the probability for 3 heads.
To find the probability of getting a certain number of heads when three coins are tossed, we can use the concept of combinations.
(a) Probability for 0 heads:
When three coins are tossed, the possible outcomes are HHT, HTH, THH, and TTT. Among these four outcomes, only one outcome has 0 heads (TTT).
Therefore, the probability of getting 0 heads is 1 out of 4 possible outcomes:
P(0 heads) = 1/4
(b) Probability for 1 head:
Among the four possible outcomes (HHT, HTH, THH, and TTT), there are three outcomes that have 1 head (HHT, HTH, and THH).
Therefore, the probability of getting 1 head is 3 out of 4 possible outcomes:
P(1 head) = 3/4
(c) Probability for 2 heads:
Among the four possible outcomes (HHT, HTH, THH, and TTT), there are three outcomes that have 2 heads (HHT, HTH, and THH).
Therefore, the probability of getting 2 heads is 3 out of 4 possible outcomes:
P(2 heads) = 3/4
(d) Probability for 3 heads:
Among the four possible outcomes (HHT, HTH, THH, and TTT), there is only one outcome that has 3 heads (HHT).
Therefore, the probability of getting 3 heads is 1 out of 4 possible outcomes:
P(3 heads) = 1/4