Question

1.A fair six-sided die is rolled. {1, 2, 3, 4, 5, 6}

Let event A = the outcome is greater than 4. Let event B = the outcome is an even number. Find P(A|B).

A.0 B.1/3 C.2/3 C.3/3

2.A student stays at home.  Let event N = the student watches Netflix. Let event Y = the student watches the very educational youtube videos made by her/his instructor.Suppose P(N) = 0.1, P(Y) = 0.8, and P(N and Y) = 0.  Are N and Y independent?

A. TRUE B. FALSE

3.A student stays at home.  Let event N = the student watches Netflix. Let event Y = the student watches the very educational youtube videos made by her/his instructor.Suppose P(N) = 0.1, P(Y) = 0.8, and P(N and Y) = 0.  Are N and Y mutually exclusive?

A. TRUE B. FALSE

4. A student stays at home.  Let event N = the student watches Netflix. Let event Y = the student watches the very educational youtube videos made by her/his instructor. Suppose P(N) = 0.1, P(Y) = 0.8, and P(N|Y) = 0.2. Find P(N and Y).

A. 0.1 B. 0.16 C. 0.18 D. 0.21 E.0.28

5. A student stays at home.  Let event N = the student watches Netflix. Let event Y = the student watches the very educational youtube videos made by her/his instructor. Suppose P(N) = 0.1, P(Y) = 0.8, and P(N|Y) = 0.2. Find P(N or Y).

A. 0.1 B.0.8 C.0. D.0.74 E.0.16

6. Alicia is playing a game by drawing a card from a standard deck and replacing it. If the card is an Ace card, Alicia win $100. If it is not an Ace card, she pay $10. There are 4 Ace cards in a deck of 52 cards.

What is the expected value of playing this game?

A. 2.934 B.-0.572 C.-1.273 D.-1.538 E.-1.792 F.-2.682

7. Alicia is playing a game by drawing a card from a standard deck and replacing it. If the card is an Ace card, Alicia win $100. If it is not an Ace card, she pay $10. There are 4 Ace cards in a deck of 52 cards.

Should Alicia play the game?

A. Yes, she is expected to win money in the long term.

B . No, she is expected to lose money in the long term.

8.Alicia is playing a game by drawing a card from a standard deck and replacing it. If the card is an Ace card, Alicia win $100. If it is not an Ace card, she pay $10. There are 4 Ace cards in a deck of 52 cards. Let X = the amount of profit. What is the standard deviation of X? (Choose the closest one)

A. 23.9556 B.29.3116 C.35.2966 D.41.9332 E.47.9814 F.53.0702 G.59.3191

9.Approximately 80% of students do their homework in time. Each student does homework independently. In a class of 40, what is the probability that 35 students will do their homework on time? Students are selected randomly.

A. 0.0001817 B.0.0167 C.0.0854 D.0.2783 E.0.8 F.0.9171

10.Approximately 80% of students do their homework in time. Each student does homework independently. In a class of 40, what is the probability that at least 39 students will do their homework on time? Students are selected randomly.

A. 0.001462 B. 0.004276 C. 0.007285 D.0.009353 E.0.032293 F.0.059264

11.Approximately 80% of students do their homework in time. Each student does homework independently. In a class of 40, how many students do you expect to do their homework in time?

A. 4 B.8 C. 12 D.24 E.32 F.36 G.40 H.80

Answer 1

1. Ans : Part B. 1/3
Reason: A fair six-sided die is rolled with outcomes [ 1,2,3,4,5,6]
It is n equally likely event since a fair die is rolled.
Thus , Each outcomes has probability of (1/6).

Probability ( X) = Number of Favourable Outcomes / Total Outcomes
Event A = Outcome is greater than 4
Outcome will be [ 5, 6]
P (A) = 2/6

Event B = Outcome is an even number
Outcome will be [ 2,4,6]
P(B) = 3/6

We need to find P(A | B)
Using Formula:
P ( A | B) = P ( A $\bigcap$ B) / P (B)
We know that,
Probability ( X) = Number of Favourable Outcomes / Total Outcomes

P ( A $\bigcap$ B) = Probability that a number is greater than 4 and even as well i.e. P ( outcome is 6)
= Number of Favourable Outcomes / Total Outcomes
P ( A $\bigcap$ ​​​​​​​ B) = 1/6

P (B) = Number of Favourable Outcomes / Total Outcomes
P (B) = 3/6

Thus, P ( A | B) = P ( A $\bigcap$ B) / P (B)
= (1/6) / (3/6)
  P ( A | B) = 1/3

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