Think about the possible outcomes of tossing a coin four times. In what situations are these outcomes obtained?
Sample Answer:
Coin Toss
Result
4 Heads
3 Heads and 1 Tail
2 Heads and 2 Tails
1 Head and 3 Tails
4 Tails
Frequency
1
4
6
4
1
Probability
1/16
1/4
3/8
1/4
1/16
Practice makes perfect
We want to find the probability distribution for four tosses of a single coin. Let's start with thinking about the possible outcomes. We can see some of the possible outcomes using this simulation.
The possible outcomes are 4 heads, 3 heads and 1 tail, 2 heads and 2 tails, 1 head and 3 tails, and 4 tails. Let's now think about the situations in which we obtain each of those outcomes. We will mark heads as H and tails as T. We will also count the possible situations for each outcome.
Coin Toss
Result
4 Heads
3 Heads and 1 Tail
2 Heads and 2 Tails
1 Head and 3 Tails
4 Tails
Possible Situations
HHHH
HHHT, HHTH, HTHH, THHH
HHTT, HTTH, TTHH, HTHT, THTH, THHT
TTTH, TTHT, THTT, HTTT
TTTT
Frequency
1
4
6
4
1
Notice that this is not based on an experiment, so the calculated probability will be theoretical. Here, we treat each outcome as equally probable, but when conducting an actual experiment the frequencies might be different. Let's now calculate the probability of each outcome. To do so we need to divide their frequencies by the total of all frequencies.
Total: 1+4+6+4+1= 16
Finally we can use this value to calculate each of the probabilities.
Coin Toss
Result
4 Heads
3 Heads and 1 Tail
2 Heads and 2 Tails
1 Head and 3 Tails
4 Tails
Possible Situations
HHHH
HHHT, HHTH, HTHH, THHH
HHTT, HTTH, TTHH, HTHT, THTH, THHT
TTTH, TTHT, THTT, HTTT
TTTT
Frequency
1
4
6
4
1
Probability
1/16
4/16=1/4
6/16=3/8
4/16=1/4
1/16
This table represents the probability distribution for 4 tosses of a coin. Note that we do not need the row Possible Outcomes in this table, so we can skip it.
Coin Toss
Result
4 Heads
3 Heads and 1 Tail
2 Heads and 2 Tails
1 Head and 3 Tails
4 Tails
Frequency
1
4
6
4
1
Probability
1/16
4/16=1/4
6/16=3/8
4/16=1/4
1/16
Since in every experiment the frequencies might be different this table is just a sample answer. However, remember that the values of theoretical probability are always the same.
