a. From a standard shuffled deck of cards, find the following probabilities:A draw of two cards without replacement that result in a face card then a fourb. The table below represents the results of gender prediction from an ultrasound Predicted MalePredicted FemaleBaby is Male7412Baby is Female1459Find the following probabilities:Correct PredictionPrediction is male given that the baby is male

Question
Asked Sep 16, 2019

a. From a standard shuffled deck of cards, find the following probabilities:

  1. A draw of two cards without replacement that result in a face card then a four

b. The table below represents the results of gender prediction from an ultrasound

 

Predicted Male

Predicted Female

Baby is Male

74

12

Baby is Female

14

59

Find the following probabilities:

  1. Correct Prediction
  2. Prediction is male given that the baby is male
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Expert Answer

Step 1

For any event A and the sample space S, the probability can be found as,

Number of Favorable cases corresponding to eventA
P(A)
Total number of cases
n(A)
n(s)
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Number of Favorable cases corresponding to eventA P(A) Total number of cases n(A) n(s)

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Step 2

Conditional rule:

The formula for probability of A given B is:

P(A B)= PAand B)
P(B)
P(Aand B)
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P(A B)= PAand B) P(B) P(Aand B)

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Step 3

a. The probability of getting a face card and then a four:

There are 12 face cards and 4 fours’ in a deck of 52 cards. The two cards are drawn one after the other without replacement. The probability of getting a face card first from the ...

P(getting a face card and a four) P(getting a face card) P(getting a four)
12
4
=
52
51
48
2,652
=0.018
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P(getting a face card and a four) P(getting a face card) P(getting a four) 12 4 = 52 51 48 2,652 =0.018

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