The probability of choosing a 6 at random from a standard deck of playing cars is 1/13.Use this information for 1 and 3.
1. what is the complement of the event of choosing a 6 ?
2. What is the probability of the complement of the event of choosing a 6 ?
3. You roll a standard number cube 1,000 times. Predict the number of times you will roll a 2 or a 5.
The probability of choosing a 6 at random from a standard deck of playing cars is 1/13.Use this information for 1 and 3.
1. what is the complement of the event of choosing a 6 ?
2. What is the probability of the complement of the event of choosing a 6 ?
3. You roll a standard number cube 1,000 times. Predict the number of times you will roll a 2 or a 5.
To answer these questions, let's break them down step by step:
1. The complement of an event refers to all the outcomes that are not part of that event. In this case, the event is choosing a 6. Since there are 52 cards in a standard deck and only 4 of them are 6s, the complement of choosing a 6 would be all the other 48 cards (52 - 4).
2. To find the probability of the complement, we need to calculate the number of favorable outcomes (the cards that are not 6s) divided by the total number of possible outcomes (all the cards in the deck). So the probability of the complement would be 48/52, which simplifies to 12/13. This means that the probability of not choosing a 6 is 12/13.
3. Rolling a standard number cube (a fair six-sided die) 1,000 times would involve independent events, meaning each roll is not affected by the previous ones. The probability of rolling a 2 or a 5 on a standard die is 2/6, or 1/3, since there are 2 favorable outcomes (rolling a 2 or a 5) out of 6 possible outcomes (rolling any number from 1 to 6).
To predict the number of times you would roll a 2 or a 5 in 1,000 rolls, you can use the concept of expected value. The expected value is equal to the probability of an event multiplied by the number of trials. So for each roll, the probability of rolling a 2 or a 5 is 1/3, and there are 1,000 rolls. Therefore, you would expect to roll a 2 or a 5 approximately (1/3) * 1,000 = 333.33 times. Since you cannot have a fractional outcome in this case, you can round it to 333 times.
In summary:
1. The complement of choosing a 6 is selecting any other card in the deck.
2. The probability of the complement is 12/13.
3. You would expect to roll a 2 or a 5 approximately 333 times out of 1,000 rolls.