Thursday is date night for Holly and David. Based on prior date nights, they will choose to go out 80% of the time. If they go out for date night, they will have steak for dinner 40% of the time, 10% of the time they will choose a pasta-based dinner, otherwise they will select something else. The probability that they will have a steak dinner is 50%. If they choose to eat at home they will only choose from pasta or steak. Answer the following questions.

(a) Determine the probability that they will have steak for dinner, given that they choose to have date night at home.
(b) Create a tree diagram based on the information given above.
(c) Find the probability that they will have steak or pasta for dinner.

The question is unclear. The statement in the question "The probability that they will have a steak dinner is 50%"... seems extra so assuming that the question is the following:

Thursday is date night for Holly and David. Based on prior date nights, they will choose to go out 80% of the time. If they go out for date night, they will have steak for dinner 40% of the time, 10% of the time they will choose a pasta-based dinner, otherwise they will select something else. If they choose to eat at home they will only choose from pasta or steak. Answer the following questions.

(a) Determine the probability that they will have steak for dinner, given that they choose to have date night at home.

(b) Create a tree diagram based on the information given above.

(c) Find the probability that they will have steak or pasta for dinner.

(a) 0.5

(b) attached in the picture

(c) 0.6

Step-by-step explanation:

(a) The first part is a conditional probability question. For that we can use the conditional probability method to find the answer. This is done in the picture attached below.

(b) Tree diagram is attached as a picture below showing all the possible outcomes.

(c)  Done in the picture below. The possible outcomes are

1- out and steak

2- out and pasta

3- home and steak

4- home and pasta

3- home and steak and 4- home and pasta have equal probability.

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5