Question

a weighted coin has a 0.472 probability of landing on heads. if you toss the coin 16 times, what is the probability of getting heads no more than 5 times?

Answer 1

To find the probability of getting heads no more than 5 times in 16 tosses of a weighted coin with a probability of 0.472 for heads, we can use the binomial probability formula.

Step-by-step explanation:

To find the probability of getting heads no more than 5 times in 16 tosses of a weighted coin with a probability of 0.472 for heads, we can use the binomial probability formula.

Let X be the random variable representing the number of heads. The probability of getting heads exactly k times out of n trials is given by:

P(X=k) = C(n, k) * p^k * q^(n-k)

where C(n, k) is the binomial coefficient, which represents the number of ways to choose k items from a set of n items. In this case, n=16, p=0.472, and q=1-p=0.528.

Now, we can calculate the probability of getting heads no more than 5 times:

1. P(X=0) = C(16, 0) * (0.472)^0 * (0.528)^(16-0)
2. P(X=1) = C(16, 1) * (0.472)^1 * (0.528)^(16-1)
3. P(X=2) = C(16, 2) * (0.472)^2 * (0.528)^(16-2)
4. P(X=3) = C(16, 3) * (0.472)^3 * (0.528)^(16-3)
5. P(X=4) = C(16, 4) * (0.472)^4 * (0.528)^(16-4)
6. P(X=5) = C(16, 5) * (0.472)^5 * (0.528)^(16-5)

Finally, we sum up these probabilities:

P(X ≤ 5) = P(X=0) + P(X=1) + P(X=2) + P(X=3) + P(X=4) + P(X=5)

Answer 2

The probability of getting heads no more than 5 times is 0.152

Using the binomial probability concept ;

• 
  `nCx * p^(x) * (1-p)^(n-x)`
• n = number of trials = 16
• x = number of successes = 5
• p = probability of success = 0.472

The probability of landing on heads no more than 5 times is ;

P(x <= 5) = p(x = 0) + .... p(x = 5)

Using the binomial probability formula ;

P(x <= 5) = 0.152

Hence, the probability of getting heads no more than 5 times is 0.152