toss two pennies. predict in 88 tosses how many times one penny will be heads and the other will be tails…
toss two pennies. predict in 88 tosses how many times one penny will be heads and the other will be tails. start by finding the probability of tossing one heads and one tails. penny 1 penny 2 toss #1: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{?}$ enter the denominator.
Answer
Explanation:
Step1: Calculate product of probabilities
When tossing two independent coins, the probability of getting heads on one and tails on the other can be calculated by considering two cases: heads on Penny 1 and tails on Penny 2 or tails on Penny 1 and heads on Penny 2. The probability of getting heads on a single - coin toss is $\frac{1}{2}$ and tails is also $\frac{1}{2}$. For the first case (heads on Penny 1 and tails on Penny 2), the probability is $\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$. Similarly, for the second case (tails on Penny 1 and heads on Penny 2), the probability is $\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$. The total probability of getting one heads and one tails is $\frac{1}{4}+\frac{1}{4}=\frac{1}{2}$.
Step2: Predict number of occurrences
We want to predict the number of times this event will occur in 88 tosses. We use the formula $n = P\times N$, where $P$ is the probability of the event and $N$ is the total number of trials. Here, $P=\frac{1}{2}$ and $N = 88$. So $n=\frac{1}{2}\times88 = 44$.
Answer:
44