Two coins were tossed 10 times. The results are shown in the table below.
result tableThe first column has the word Toss in the 1st Row and the word Results in the second row. The second column has the number 1 in the 1st Row and the letters H H in the 2nd Row. The third column has the number 2 in the 1st Row and the letters T T in the 2nd Row. The fourth column has the number 3 in the 1st Row and the letters H T in the 2nd Row. The fifth column has the number 4 in the 1st Row and the letters T H in the 2nd Row. The sixth column has the number 5 in the 1st Row and the letters H T in the 2nd Row. The seventh column has the number 6 in the 1st Row and the letters H H in the 2nd Row. The eighth column has the number 7 in the 1st Row and the letters T H in the 2nd Row. The ninth column has the number 8 in the 1st Row and the letters T T in the 2nd Row. The tenth column has the number 9 in the 1st Row and the letters T H in the 2nd Row. The eleventh column has the number 10 in the 1st Row and the letters H T in the 2nd Row.
Make a tree diagram for two coins that are tossed. Find the theoretical probability that at least one coin is heads. Express the probability as a decimal.
Tree diagram:
Toss 1
/ \
H T
/ \ / \
Toss 2 H Toss 2 T
/ \ / \
H T H T
Theoretical probability that at least one coin is heads:
There are three outcomes in which at least one coin is heads: HH, HT, TH. These outcomes occur 6 times in the 10 tosses. Therefore, the probability is 6/10 or 0.6.
To create a tree diagram for two coins being tossed, we start by branching out from the starting point, which represents the first coin toss. We draw two branches labeled H (heads) and T (tails) for the possible outcomes of the first coin.
```
Toss 1
/ \
H T
```
From each branch representing the outcomes of the first coin toss, we draw two new branches for the second coin toss, one for each possible outcome.
```
Toss 1
/ \
H T
| |
(H, H) (T, H)
```
```
Toss 1
/ \
H T
| |
(H, H) (T, H)
| |
(H, T) (T, T)
```
Now we have a complete tree diagram for two coins being tossed.
To find the theoretical probability that at least one coin is heads, we count the number of outcomes where at least one coin is heads. In this case, there are 5 outcomes where at least one coin is heads: (H, H), (H, T), (T, H), (H, T), (T, H).
Since there are a total of 4 outcomes, the probability of getting at least one heads is 5/4, which simplifies to 1.25 as a decimal.