The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next 6 months is

Question

Mathematics

Ellie Stuart

24 January, 21:43

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. The probability that both house sales and interest rates will increase during the next 6 months is

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Lucy · Answer 1

The probability that both house sales and interest rates will increase during the next 6 months is 0.1.

Step-by-step explanation:

Consider the provided information.

The probability that house sales will increase in the next 6 months is 0.25. The probability that the interest rates on housing loans will go up in the same period is 0.74. The probability that house sales or interest rates will go up during the next 6 months is 0.89.

Therefore,

Probability that house sales will increase = P (A) = 0.25

Probability that the interest rates on housing loans = P (B) = 0.74

The probability that house sales or interest rates will go up during = P (AUB) = 0.89

The probability that both house sales and interest rates = P (A∩B)

Now, use the formula:

P (A∩B) = P (A) + P (B) - P (AUB)

Substitute the respective value in the above formula.

P (A∩B) = 0.25+0.74-0.89 = 0.1

Hence, the probability that both house sales and interest rates will increase during the next 6 months is 0.1.