NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.3 Question 10

Question

A girl rolls a fair die. On 5 or 6 she tosses a coin three times, otherwise once. Given exactly one head, find P(die was 1,2,3 or 4).

Accepted Answer

Final Answer: die 1–4: 8/11 Step 1: Use the mutually exclusive source events with prior probabilities die 1–4=2/3, die 5–6=1/3. Step 2: One toss gives exactly one head with probability 1/2. Three fair tosses give exactly one head in three of eight strings, hence probability 3/8. Step 3: The observation likelihoods in the same order are 1/2, 3/8. Multiply each prior by its likelihood to get joint probabilities 1/3, 1/8. Step 4: Total probability of the observation is 1/3 + 1/8 = 11/24. Step 5: Bayes: P(die 1–4 | observation) = 1/3 / 11/24 = 8/11.

NCERT Class 12 Maths · Chapter 13 Probability · Exercise 13.3 Question 10

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