Question

The USF Student Government has seven elected student representatives. Each student representative is equally likely to serve in any of the positions. What is the probability of randomly selecting a President and a vice president?

Group of answer choices 0.024 0.33 0.033 0.002

2. Consider a deck of cards. What is the probability that we observe a red even number card for the first time on the 2nd or 5th draw?

Group of answer choices

0.125

0.237

0.207

0.08

Thirty percent of adults strongly believe the news from social media. You randomly select five adults. Find the probability that the number of adults who strongly believe the news from social media is less than three.

Group of answer choices

0.132

0.163

0.837

0.969

Answer 1

Dear student, we can solve one question at a time, please help to upload other questions separately. Here, I am answering question 1.

1.

P(A) = n(E)/n(S)

Where P(A) is the probability of an event A

n(E) is the number of favorable outcomes

n(S) is the total number of events in the sample space.          

There are 7 student representatives and positions are two.

Probability of 1 getting selected as the president = 1 / 7

Probability of 1 getting selected as the vice-president = 1 / 6 (as 1 is already selected as the president, he/she can not be selected as a vice-president also).

These are two independent events.

Probability of randomly selecting a President and a vice president = (Probability of 1 getting selected as the president) * (Probability of 1 getting selected as the vice-president)

Probability of randomly selecting a President and a vice president = (1 / 7)*(1 / 6) = 0.0238.

Option A is the right answer here.