Flipping a Coin
Frequency
Heads 27
Tails 23
Nigel flips a coin 50 times and records whether it lands on heads or tails. What is the experimental probability that the coin will land on heads?
Responses
The experimental probability of the coin landing on heads is:
27 (number of times heads appeared) / 50 (total number of coin flips) = 0.54 or 54%
Johanna is trying to find the probability that a cup will land open end up. She takes a cup and tosses it in the air 100 times and each time records if it lands open end up or open end down. She finds that 63 times the cup lands open end up. What is the probability that the cup will land open end down?
Since there are only two possible outcomes (the cup lands open end up or open end down), the probability of the cup landing open end down is:
1 - (63/100) = 37/100 = 0.37 or 37%
We subtract 63/100 from 1 because the sum of the probabilities of all possible outcomes must equal 1.
Johanna is trying to find the probability that a cup will land open end up. She takes a cup and tosses it in the air 1000 times and each time records if it lands open end up or open end down. She finds that 630 times the cup lands open end up. Do the outcomes of the cup appear to be equally likely?
To determine if the outcomes appear to be equally likely, we need to compare the experimental probability (the proportion of times the cup landed open end up in Johanna's 1000 trials) to the theoretical probability (the expected proportion of times the cup would land open end up if the outcomes were equally likely).
The theoretical probability of the cup landing open end up if the outcomes were equally likely would be 1/2, since there are two possible outcomes and each would be equally likely.
To compare, we can calculate the experimental probability:
630/1000 = 0.63 or 63%
Since the experimental probability is close to the theoretical probability of 1/2 (50%), we can conclude that the outcomes of the cup appear to be equally likely.
To find the experimental probability of an event, we divide the number of times the event occurred by the total number of trials. In this case, Nigel flipped the coin 50 times.
Given that the coin landed on heads 27 times out of the 50 flips, we can calculate the experimental probability as follows:
Experimental Probability (Heads) = Number of Heads / Total Number of Trials
Plugging in the values, we get:
Experimental Probability (Heads) = 27 / 50
Calculating the value, we find:
Experimental Probability (Heads) = 0.54 or 54%
Therefore, the experimental probability that the coin will land on heads is 0.54 or 54%.