Each member of the group toss 4 coins 10 times and observe how many heads are shown. Then combine all observations. a.Create a frequency table displaying the results. (9 marks) b.Compare the frequency table to the theoretical probability distribution for the outcome when 4 coins are tossed. (5 marks) Find the mean for the frequency table. Compare your answer with the mean for the probability distribution and give the interpretation.
Answers
Given : Each 4 member of the group toss 4 coins 10 times and observe how many heads are shown.
To find : Probability Distribution
Solution:
Do the Experiment yourself.
I am Finding here theoretical Probability Distribution
P(H) = 1/2
P(T) = 1/2
4 Coins
Probability of 0 Heads 4 Tails = ⁴C₀(1/2)⁰(1/2)⁴ = 1/16
Probability of 1 Heads 3 Tails = ⁴C₁(1/2)¹(1/2)³ = 4/16 = 1/4
Probability of 2 Heads 2 Tails = ⁴C₂(1/2)²(1/2)² = 6/16 = 3/8
Probability of 3 Heads 1 Tails = ⁴C₃(1/2)³(1/2)¹ = 4/16 = 1/4
Probability of 4 Heads 0 Tails = ⁴C₄(1/2)⁴(1/2)⁰ = 1/16
Mean Head = 0 * 1/16 + 1*4/16 + 2*6/16 + 3*4/16 + 4*1/16
= (0 + 4 + 12 + 12 + 4) /16
= 32/16
= 2
Now 10 Time This process is repeated
Probability of 0 Head or 4 Heads for x Times ( x from 0 to 10 here)
P(x) = ¹⁰Cₓ(1/16)ˣ(15/16)ⁿ⁻ˣ
Probability of 1 Head or 3 Heads for x Times
P(x) = ¹⁰Cₓ(1/4)ˣ(3/4)ⁿ⁻ˣ
Probability of 2 Head for x Times
P(x) = ¹⁰Cₓ(3/8)ˣ(5/8)ⁿ⁻ˣ
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