Each 4 member of the group toss 4 coins 10 times and observe how many heads are shown. Then combine all observations. a. Create the 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) c. Find the mean for the frequency table. Compare your answer with the mean for the probability distribution and give the interpretation.
Answers
Answer:
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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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