Question

An unbiased coin is tossed 15 times.

1. Find the probability that the coin lands heads exactly 9 times. a. 0.0003 b. 0.3571 c. 0.6429 d. 0.1527 e. 0.4213

2. Find the probability that the coin lands tails at most 3 times. a. 0.0002 b. 0.0037 c. 0.5000 d. 0.0176 e. 0.8723

3. Find the probability that the coin lands heads at least 3 times. a. 0.0005 b. 0.9963 c. 0.9333 d. 0.0003 e. 0.8890

A computer stores receives a box of a certain video game. The box contains 35 games of which 4 are defective. A quality-control inspector randomly chooses 6 games from the box.

4. What is the probability that exactly 2 are defective? a. 0.0111 b. 0.0075 c. 0.1667 d. 0.8333 e. 0.1163

5. What is the probability that 0 are defective? a. 0.05410 b. 0.45361 c. 0.15473 d. 0.00029 e. 0.92445

6. What is the probability that at most 3 are defective? a. 0.9997 b. 0.6102 c. 0.5464 d. 0.8957 e. 0.2189

Carrie draws 5 cards simultaneously from a well-shuffled deck of 52 playing cards.

7. What is the probability that she chooses 3 spades and 2 cards that are not spades? a. 0.7692 b. 0.0782 c. 0.2308 d. 0.2743 e. 0.0815

8. What is the probability that she chooses 2 red face cards? a. 0.4308 b. 0.2273 c. 0.0876 d. 0.0962 e. 0.1736 Use the following problem to answer questions 9 and 10. A group of 27 people contains 13 males and 14 females. Six people are chosen at random.

9. What is the probability that 1 female is chosen? a. 0.1826 b. 0.0011 c. 0.0654 d. 0.3442 e. 0.0609

10. What is the probability that at most 1 male is chosen? a. 0.3021 b. 0.0981 c. 0.0909 d. 0.2044 e. 0.6596

Answer 1

1)

probability that the coin lands heads exactly 9 times=¹⁵C₉(0.5)⁹(0.5)⁶ =0.1527

2)probability that the coin lands tails at most 3 times=0.0176

3) probability that the coin lands heads at least 3 times=0.9963

4) probability that exactly 2 are defective=0.1163

5)probability that 0 are defective=0.4536

6)probability that at most 3 are defective =0.9997

7)probability that she chooses 3 spades and 2 cards that are not spades=0.0815

8)probability that she chooses 2 red face cards=0.0876

9) probability that 1 female is chosen=0.0609

10) probability that at most 1 male is chosen=0.0981