Find The Interest Refund On A 35-month Loan With Interest Of $2,802 If The Loan Is Paid In Full With
The probability of getting at least 60 heads in 100 tosses is the sum of these probabilities multiplied by the number of ways to get at least 60 heads (C(100, 60)).
To find the probability of winning at least $20 after 100 coin tosses, we can use the binomial distribution.
In this case, we want to find the probability of getting at least 10 more heads than tails, since each head gives us $2 and each tail takes away $2.
Let’s break down the problem step by step:
1. Calculate the probability of getting a head (H) or a tail (T) in a single coin toss:
The probability of getting a head (H) is 1/2.
The probability of getting a tail (T) is also 1/2.
2. Determine the number of ways to get at least 20 more heads than tails in 100 tosses:
To win at least $20, we need to get 60 or more heads (since 60 heads would result in $120, which is $20 more than 40 tails).
We can use the binomial coefficient formula to calculate this. The formula is:
C(n, k) = n! / (k!(n-k)!)
In our case, n is 100 (the number of tosses) and k is 60 (the minimum number of heads we need).
Therefore, C(100, 60) = 100! / (60!(100-60)!).
3. Calculate the probability of getting at least 60 heads in 100 tosses:
The probability of getting exactly 60 heads is (1/2)^60.
The probability of getting exactly 40 tails is (1/2)^40.
The probability of getting at least 60 heads in 100 tosses is the sum of these probabilities multiplied by the number of ways to get at least 60 heads (C(100, 60)).
To find the final probability, you would need to calculate the sum of the probabilities for getting 60, 61, 62, …, 100 heads, and add them all together.
The actual calculation for all these probabilities is quite extensive and time-consuming. It is recommended to use statistical software or calculators with binomial distribution functions to get accurate results.
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