Patty tosses a coin and rolls a number cube.
1)Find the probability that the coin lands on heads and the cube lands on an even number
2)Patty tosses the coin and rolls the number cube 60 times. Predict how many times the coin will land on Heads and the cube will land on an even number
1) You have to multiply the probability of each thing occurring, that will be your correct response.
2. multiply the probability you found in 1. by 60
I got 2/16 but I’m bad at math so idk
To find the probability of two independent events occurring together, we need to multiply the probabilities of each individual event.
1) Find the probability that the coin lands on heads and the cube lands on an even number:
Step 1: Determine the probability of the coin landing on heads.
Since there are two possible outcomes (heads or tails) and assuming a fair coin, the probability of the coin landing on heads is 1/2.
Step 2: Determine the probability of the cube landing on an even number.
A standard number cube has six sides numbered from 1 to 6. Out of these six numbers, three (2, 4, and 6) are even.
So, the probability of rolling an even number is 3/6, which simplifies to 1/2.
Step 3: Multiply the probabilities of each event to find the probability of both events occurring.
P(coin landing on heads and cube landing on an even number) = P(coin landing on heads) x P(cube landing on an even number)
= 1/2 x 1/2
= 1/4
Therefore, the probability that the coin lands on heads and the cube lands on an even number is 1/4 or 25%.
2) To predict the number of times both events will occur when Patty tosses the coin and rolls the cube 60 times, we can use the expected value.
Step 1: Calculate the expected value for each individual event.
The expected value of tossing a fair coin and getting heads is given by:
Expected value (coin landing on heads) = Probability(coin landing on heads) x Number of trials
= (1/2) x 60
= 30
Similarly, the expected value of rolling a number cube and getting an even number is given by:
Expected value (cube landing on an even number) = Probability(cube landing on an even number) x Number of trials
= (1/2) x 60
= 30
Step 2: Predict the number of times both events will occur.
Since the events are independent, we can add the expected values together:
Expected value (coin landing on heads and cube landing on an even number) = Expected value (coin landing on heads) + Expected value (cube landing on an even number)
= 30 + 30
= 60
Therefore, if Patty tosses the coin and rolls the number cube 60 times, we can predict that the coin will land on heads and the cube will land on an even number approximately 60 times.