Question

Q1

Step 1. Flip a fair coin. Step 2. If you got a head in step 1, flip two fair coins. If you got a tail in step 1, flip one fair coin. Given that you got only tails in step 2. what is the chance that you got tails in step 1? Round your answer to nearest .xx

Q2

Q3

Answer 1

1)

Sample Space

[TH] [TT] [HHH] [HTH] [HHT][HTT]

Probability of you got tails in step 1 =  2/6

= 1/3

2)

Probability of same number = 1/60 * 1/60 * 1/60 * 1/60 * 1/60 * 60

Probability of differet number = 1- 1/60 * 1/60 * 1/60 * 1/60 * 1/60 * 60

= 0.9999

3)

Ho :   σ² =   4
Ha :   σ² >   4
      
Level of Significance ,    α =    0.1
sample Variance,   s² =    7.29
Sample Size ,   n =    20
      
Chi-Square Statistic   X² = (n-1)s²/σ² =    34.6275
      
degree of freedom,   DF=n-1 =    19
      
one tail test       
Upper Critical Value   =   27.204
p-Value   =   0.015

Ο 0.01 <ρ< 0.025

Please let me know in case of any doubt.

Thanks in advance!

Please upvote!