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

Answer:

Event       Probability

Heads          $\dfrac{3}{5}$

Tails             $\dfrac{2}{5}$

Step-by-step 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,

$Probability=\dfrac{\text{Favorable outcomes}}{\text{Total number of outcomes}}$

$P(H)=\dfrac{\text{Number of heads}}{\text{Total number of tosses}}=\dfrac{15}{25}=\dfrac{3}{5}$

$P(T)=\dfrac{\text{Number of tails}}{\text{Total number of tosses}}=\dfrac{10}{25}=\dfrac{2}{5}$

So, probability distribution table is

Event       Probability

Heads          $\dfrac{3}{5}$

Tails             $\dfrac{2}{5}$

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

Since,

$\dfrac{3}{5}+\dfrac{2}{5}=\dfrac{3+2}{5}=\dfrac{5}{5}=1$

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