The problem asks us to calculate the probability of two events: (1) The customer randomly selects a sweater or a hat. (2) The customer randomly selects a jacket. The store has 5 hats, 10 jackets, 15 pants, and 20 sweaters. We are given the probability choices: 0.10, 0.20, 0.40, 0.50, 0.70, 0.80.

1. Problem Description

The problem asks us to calculate the probability of two events:

(1) The customer randomly selects a sweater or a hat.

(2) The customer randomly selects a jacket.

The store has 5 hats, 10 jackets, 15 pants, and 20 sweaters. We are given the probability choices: 0.10, 0.20, 0.40, 0.50, 0.70, 0.

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2. Solution Steps

First, find the total number of items on sale.

$Total = 5 \text{ hats} + 10 \text{ jackets} + 15 \text{ pants} + 20 \text{ sweaters} = 50 \text{ items}$

Next, calculate the probability of selecting a sweater or a hat.

$P(\text{sweater or hat}) = P(\text{sweater}) + P(\text{hat}) = \frac{\text{number of sweaters}}{\text{total items}} + \frac{\text{number of hats}}{\text{total items}} = \frac{20}{50} + \frac{5}{50} = \frac{25}{50} = \frac{1}{2} = 0.50$

Then, calculate the probability of selecting a jacket.

$P(\text{jacket}) = \frac{\text{number of jackets}}{\text{total items}} = \frac{10}{50} = \frac{1}{5} = 0.20$

3. Final Answer

The probability that the customer will randomly select a sweater or a hat is 0.

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0. The probability that the customer will randomly select a jacket is 0.20.