Question

6. Create a probability distribution for a coin flipping game. That is, toss a coin at least 25 times and keep up with the number of heads and the number of tails. (8 points for each part) a. Compile your data into a probability distribution. Be sure to show that your distribution meets the properties for a probability distribution. Trial 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Res. T H H H T H H H H T H H T H T H T T H T T H H T H H 15/25=3/5 T 10/25=2/5 3/5+2/5=1 Can anyone help with part a im lost!

Answer 1

Event Probability

Heads
`(3)/(5)`

Tails
`(2)/(5)`

Explanation:

If a coin is tossed 25 times, then from the given table it is clear that

Number of heads = 15

Number of tails = 10

Total number of tosses = 15+10 = 25

We know that,

`Probability=\frac{\text{Favorable outcomes}}{\text{Total number of outcomes}}`

`P(H)=\frac{\text{Number of heads}}{\text{Total number of tosses}}=(15)/(25)=(3)/(5)`

`P(T)=\frac{\text{Number of tails}}{\text{Total number of tosses}}=(10)/(25)=(2)/(5)`

So, probability distribution table is

Event Probability

Heads
`(3)/(5)`

Tails
`(2)/(5)`

According to the properties for a probability distribution, the sum of probability of all events is 1.

Since,

`(3)/(5)+(2)/(5)=(3+2)/(5)=(5)/(5)=1`

Hence, the distribution meets the properties for a probability distribution.