Please check my answers
Would you be more likely to get at least 70% tails if you flip a fair coin 10 times or if you flip a fair coin 1000 times? same
Consider a bowl containing 36 different slips of paper. Ten of the slips of paper each contain one of the digits from the set 0 through 9 and 26 slips each contain one of the 26 letters of the alphabet. If one slip is drawn at random, what is P(a number that is not prime appears on the slip)? 5/36
Consider the experiment of rolling a single die. Find the probability of the event described.
15)
What is P(odd and prime)?
1/2
)
Suppose a basketball player is an excellent free throw shooter and makes 91% of his free throws (i.e., he has a 91% chance of making a single free throw). Assume that free throw shots are independent of one another. Suppose this player shoots five free throws. Find the probability that he makes all five throws.
18)
______
A) 0
B) 0.376
C) 0.624
D) 1
I got c
Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What is the probability that the second card is a spade if the first card was not a spade? 1/4
A die is rolled twice. What is the probability of getting a sum greater than or equal to ten?
1/6
Yes, Same.
Not prime number between 0-9 are 4, 6 and 8 --> 3/36
I got c too.
not spade = 39/52 * 13/51 = ?
I get 1/6 too.
Let's go through your answers one by one to check if they are correct:
1. Would you be more likely to get at least 70% tails if you flip a fair coin 10 times or if you flip a fair coin 1000 times? You mentioned that it is the same likelihood. That is correct. The probability of getting at least 70% tails would be the same whether you flip a coin 10 times or 1000 times, as long as the coin is fair.
2. Consider a bowl containing 36 different slips of paper. Ten of the slips of paper each contain one of the digits from the set 0 through 9, and 26 slips each contain one of the 26 letters of the alphabet. If one slip is drawn at random, you mentioned that the probability of drawing a number that is not prime is 5/36. That is correct. Since there are 10 slips with digits from 0 to 9, and 4 of them are prime (2, 3, 5, 7), the number of slips with numbers that are not prime would be 10 - 4 = 6. Therefore, the probability of drawing a number that is not prime is 6/36, which simplifies to 1/6 or approximately 0.1667.
3. Consider the experiment of rolling a single die. You mentioned that the probability of rolling an odd and prime number is 1/2. That is not correct. Let's break it down. There are six possible outcomes when rolling a die: 1, 2, 3, 4, 5, and 6. Out of these six, only three are odd and prime numbers: 3, 5, and 1 (since 1 is not considered prime, but it is odd). Therefore, the probability of rolling an odd and prime number is 3/6, which simplifies to 1/2 or 0.5.
4. Suppose a basketball player is an excellent free throw shooter and makes 91% of his free throws. You mentioned that the probability that he makes all five throws is 0.624, option C. That is not correct. Let's calculate the probability. Since each free throw is independent, the probability of making a single free throw is 0.91. Therefore, the probability of making all five throws would be 0.91^5, which equals approximately 0.624 or 62.4%. Option C is the correct answer.
5. Two cards are drawn without replacement from an ordinary deck of 52 playing cards. What is the probability that the second card is a spade if the first card was not a spade? You mentioned that the probability is 1/4. That is not correct. Let's calculate it. In a standard deck, there are 13 spades out of 52 cards. If the first card is not a spade, there are 39 non-spade cards left out of 51 cards. Therefore, the probability of drawing a spade as the second card is 13/51, which simplifies to approximately 0.255 or 25.5%.
6. A die is rolled twice. You mentioned that the probability of getting a sum greater than or equal to ten is 1/6. That is not correct. Let's calculate it. There are 36 possible outcomes when rolling two dice, and out of those, there are 3 favorable outcomes where the sum is greater than or equal to ten: (4, 6), (5, 5), and (6, 4). Therefore, the probability of getting a sum greater than or equal to ten would be 3/36, which simplifies to 1/12 or approximately 0.0833.
You have some correct answers, but there are a few that need corrections.