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vodka [1.7K]
4 years ago
12

Lara tossed a fair coin 3 times. What is the probability of getting heads in the first two trials? 1 over 8 2 over 8 3 over 8 4

over 8
Mathematics
1 answer:
Dovator [93]4 years ago
7 0
4/8 is equal to 1/2. While this is true of one coin toss, it is not a 50% chance if you toss the coin twice. In tossing the coin twice you have the options of: heads, tails, heads, tails (One head and one tail per coin). Since there are four options, it is a 25% chance you will get heads twice in a row. 25% equals 1/4 which equals 2/8.
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Prof B and Prof D

Step-by-step explanation:

Step-by-step explanation:

From the question  we are told that

Sample size 100  

Instructor    Number of Failures  

Prof. A         13

Prof. B         0

Prof. C         11

Prof. D         16

Confidence level= 0.95

From Z table

Z=1.96

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  Proportion\ of\ Failure\ P=\frac{Number\ of\ Failure\ N}{Sample\ size\ S}

  P=\frac{N}{S}

For Prof A

    P_A=\frac{N_A}{S}

    P_A=\frac{13}{100}

    P_A=0.13

For Prof B

    P_B=\frac{N_B}{S}

   P_B=\frac{0}{100}

    P_B=0

For Prof C

    P_C=\frac{N_C}{S}

    P_C=\frac{11}{100}

   P_C=0.11

For Prof D

     P_D=\frac{N_D}{S}

   P_D=\frac{16}{100}

   P_D=0.16

Generally the average proportional failure is mathematically given as

    P_a_v_g=\frac{0.13+0+0.11+0.16}{4}

   P_a_v_g=0.10

Therefore  having this we calculate for the control limits

Generally the upper control limit UCl is mathematically given as

Upper control limits:

  UCL =P_a_v_g +Z\sqrt{\frac{P_a_v_g(1-P_a_v_g) }{S} }

  UCL =0.1 +1.96\sqrt{\frac{0.1(1-0.1) }{100}}

  UCL =0.1 +1.96*0.03

  UCL =0.1 +0.0588

  UCL =0.1588

Generally the upper control limit UCl is mathematically given as

Lower limit control limits:

 UCL =P_a_v_g _Z\sqrt{\frac{P_a_v_g(1-P_a_v_g) }{S} }

 UCL =0.1 -1.96\sqrt{\frac{0.1(1-0.1) }{100}}

  UCL =0.1 -1.96*0.03

  UCL =0.1 -0.0588

  UCL =0.0412

Therefore the Range is 0.0412 to 0.1588

Given the range 0.0412 to 0.1588 Prof B and Prof D are outside the Range making them the correct options

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