Question

Jing and Bob are each invited to a party. From previous experience, it is known that there is a 95% probability that at least one of them will actually go to the party. In addition, Jing will actually go to the party with 80% probability, and Bob will actually go to the party with 75% probability. Based on this information, you are asked to determing what can be said about these two events: Event 1: "Jing will actually go to the party" and Event 2: "Bob will actually go to the party" Q1) Are these two events complementary events? Q2) Are these two events disjoint (or mutually exclusive) events? Q3) Are these two events independent events?

Answer 1

Answer:

Q1. these two events aren't complementary events

Q2. these two events aren't disjoint (or mutually exclusive) events

Q3. These two events are independent events

Step-by-step explanation:

First, we need to understand the the 95% probability that at least one of them will actually go to the party is calculate as:

P = (0.8)(0.25) + (0.2)(0.75) + (0.8)(0.75) = 0.95

Where (0.8)(0.25) is the probability that Jing will go to the party and Bob won't, (0.2)(0.75) is the probability that Jing won't go to the party and Bob will and (0.8)(0.75) is the probability that Jing and Bob will go to the party.

it means that there are 3 possibles results:

1. Jing will go to the party and Bob won't (Event 1)

2. Jing won't go to the party and Bob will (Event 2)

3. Jing and Bob will go to the party (Event 1 and Event 2)

So, Event 1 and event 2 are not complementary because they are not the only possible results.

Additionally, these events are not disjoint because event 1 and event 2 can happen simultaneously.

Finally, they are independent because the probability that event 1 happens does not affect the probability that event 2 happens.