Question

Alex tells the truth 70% of the time while Blake tells the truth 80% of the time, independently of each other. They are shown an apple and asked "Is it an apple or a banana?". What is the probability that they will give different answers?

Answer 1

Question :–

▪︎ Alex tells the truth 70% of the time while Blake tells the truth 80% of the time, independently of each other. They are shown an apple and asked "Is it an apple or a banana?". What is the probability that they will give different answers ?

ANSWER :–

GIVEN :–

• Probability when Alex tells the truth = 70% = 0.7

• Probability when Blake tells the truth = 80% = 0.8

TO FIND :–

• Probability will they will give different answers = ?

SOLUTION :–

▪︎ Probability when Alex tells the truth (p) = 0.7

• Probability when Alex tells false (p') = 1 - 0.7 = 0.3

▪︎ Probability when Blake tells the truth (q) = 0.8

• Probability When Blake tells the false (q') = 1 - 0.8 = 0.2

▪︎ Now According to the question –

⇒ Required probability = Alex and Blake give Differentiate answer

⇒ Required probability = (p)(q') + (q)(p')

⇒ Required probability = (0.7)(0.2) + (0.8)(0.3)

⇒ Required probability = 0.14 + 0.24 = 0.38

➪ Hence , probability when they will give different answer is 0.38