Chapter 5: Q 14. (page 295)

Stoplight On her drive to work every day, Ilana passes through an intersection with a traffic light. The light has a probability of 1/3 of being green when she gets to the intersection. Explain how you would use each chance device to simulate whether the light is red or green on a given day.
(a) A six-sided die
(b) Table D of random digits
(c) A standard deck of playing cards

Short Answer

Expert verified

Part (a) If the upper side's number of dots is $1, 2$ she obtains a green light.

Part (b) She gets a green light if the number of dots on the upper side is $1, 2, 3$

Part (c) The heart sign appears on the card, and she is given a green light.

Step by step solution

Part (a) Step 1.Given

When Ilana arrives at the intersection, there's a $1 / 3$ chance that a light will be green.

Part (a) Step 2. Concept Used

Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Part (a) Step 3. Explanation

Using six-sided dice, we employed each chance gadget to stimulate whether the light is red or green on a specific day. Toss in the six-sided dice and see what happens. If the number of dots on the upper side is $1$ or $2$ she gets a green light. If the number of dots on the upper side is $3, 4, 5, 6$ she does not get a green signal. As a result, if the number of dots on the upper side is $1$ or $2$ we know she gets a green light.

Part (b) Step 1. Explanation

We have used each chance gadget to stimulate whether the light is red or green on a certain day using Table Do of random numbers.

Take a look at table D and pick a row.

She gets a green light if the digit is a $1, 2, 3$

She doesn't get a green signal if the digit is $4, 5, 6, 7, 8, 9$

If the digit is zero, disregard it and proceed to the next.

As a result, we know that if the digit is a $1, 2, 3$ she will be given the green light.

Part (c) Step 1. Explanation

Using a standard deck of playing cards, we used the each chance gadget to simulate whether the light is red or green on a given day. Choose a card from a standard deck of cards. You have a $50 / 50$ chance of picking a suit from a deck of cards (hearts, diamonds, spades, or clubs) If the card has a heart symbol on it, she gets a green light. If the card has a diamond or spade sign on it, she does not obtain a green light. If the card has a club symbol on it, you must draw another card. As a result, we know that she will get a green signal if the card has a heart symbol on it.