You are going to toss 2 pennies 20 times. Make a prediction. how many times do you think the 2 pennies will come up as:
2 heads:
2 tails:
1 head, 1 tail:
You can pick any number: it is a prediction. In 20 times, the distribution will be binomial, and it will vaguely look like a normal distribution, if one did it 2000 times, it would look much more normal.
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To make a prediction for the outcomes of tossing 2 pennies 20 times, we can use probability. Let's consider the possible outcomes for each toss of the 2 pennies:
1. Outcomes for 2 heads: In each coin toss, the probability of getting a head is 1/2. When tossing 2 pennies, the probability of getting 2 heads is (1/2) * (1/2) = 1/4. So, for each toss, there is a 1/4 chance of getting 2 heads.
2. Outcomes for 2 tails: Similarly, the probability of getting a tail in each coin toss is 1/2. When tossing 2 pennies, the probability of getting 2 tails is (1/2) * (1/2) = 1/4. So, for each toss, there is a 1/4 chance of getting 2 tails.
3. Outcomes for 1 head, 1 tail: In this case, there are two possible outcomes: getting a head and a tail (HT) or getting a tail and a head (TH). The probability of each outcome is (1/2) * (1/2) = 1/4. So, for each toss, there is a 1/4 chance of getting 1 head and 1 tail.
Considering these probabilities, we can predict the expected number of outcomes for each scenario by multiplying the probability by the number of tosses:
1. Expected number of 2 heads: (1/4) * 20 = 5
2. Expected number of 2 tails: (1/4) * 20 = 5
3. Expected number of 1 head, 1 tail: (1/4) * 20 = 5
Therefore, based on these probabilities, we can predict that out of 20 tosses of 2 pennies:
- The 2 pennies will likely come up as 2 heads around 5 times.
- The 2 pennies will likely come up as 2 tails around 5 times.
- The 2 pennies will likely come up as 1 head and 1 tail around 5 times.