Question

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) c. Find the mean for the frequency table. Compare your answer with the mean for the probability distribution and give the interpretation. (6 marks)

Answer 1

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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