A coin is tossed 10 times. What is the probability that the third head will apear on the tenth toss?
To find the probability of the third head appearing on the tenth toss, we need to determine the number of possible outcomes that satisfy the condition, divided by the total number of possible outcomes.
Let's break down the problem into smaller steps:
Step 1: Calculate the total number of possible outcomes
When a coin is tossed, it can either land as heads or tails. Since each toss has two possible outcomes, and we are tossing the coin 10 times, the total number of possible outcomes can be calculated as 2^10 = 1024.
Step 2: Calculate the number of outcomes where the third head appears on the tenth toss
Since we want to determine the probability of the third head appearing on the tenth toss, the previous nine tosses can result in any combination of heads or tails. However, the tenth toss must be a head. This implies that we have only one option for the tenth toss to be a head.
Let's consider the position of the third head. Since there are 10 tosses, there are 9 possible positions for the third head. Thinking of these positions as slots, we need to select one of the slots to put the third head in.
Therefore, the number of outcomes where the third head appears on the tenth toss is 9.
Step 3: Calculate the probability
Now, we can calculate the probability by dividing the number of favorable outcomes (in step 2) by the total number of possible outcomes (in step 1).
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 9 / 1024
To simplify the fraction, we can find the highest common factor (HCF) of 9 and 1024, which is 1.
So, the probability that the third head will appear on the tenth toss is 9/1024, or approximately 0.0088.