An automobile tire dealer buys tires in lots of 750. His experience is that 1% of all new tires purchased must be replaced within 30 days as they are defective. Find the probability that in a lot of 750 tires, there will be a) No defective tires ( 3 Marks) b) Less than two defective tires

a. 5.33 × 10⁻⁴ b. 4.568 × 10⁻³

Step-by-step explanation:

a. This situation represents a binomial probability. Let p = probability that tire is defective = 1% = 0.01, then q = probability that tire is not defective = 1 - p = 1 -   0.01 = 0.99 = 99%.

Since there are 750 tires, the probablility that no tire is defective is P = ⁷⁵⁰C₀q⁷⁵⁰p⁰

= (1) (0.99)⁷⁵⁰(0.01)⁰

= 5.33 × 10⁻⁴

b. The probability that less than two tires will be defective P'

So, P' = ⁷⁵⁰C₀q⁷⁵⁰p⁰ + ⁷⁵⁰C₁q⁷⁴⁹p¹

= (1) (0.99)⁷⁵⁰(0.01)⁰ + (750)(0.99)⁷⁴⁹(0.01)¹

= 5.33 × 10⁻⁴ + 0.004035

= 45.68 × 10⁻⁴

=  4.568 × 10⁻³

there will be 35 boys in each team. : )

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.