Question

A biased coin, with a probability of heads (P(heads)) equal to 0.9 and tails (P(tails)) equal to 0.1, is tossed 10 times. What is the probability of getting exactly 3 heads?

A) 0.0574
B) 0.0572
C) 0.0576
D) 0.0578

Answer 1

To calculate the probability of getting exactly 3 heads when a biased coin is tossed 10 times, use the binomial probability formula with p = 0.9 and q = 0.1. The probability is 0.0574. Thus the correct option is A) 0.0574.

Explanation:

To calculate the probability of getting exactly 3 heads when a biased coin with P(heads) = 0.9 and P(tails) = 0.1 is tossed 10 times, we can use the binomial probability formula.

The formula is:

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

Where:

• P(X = k) is the probability of getting exactly k heads
• C(n, k) is the number of ways to choose k heads from n tosses (which can be calculated using the combination formula)
• p is the probability of getting a head (0.9 in this case)
• q is the probability of getting a tail (0.1 in this case)
• Using this formula, we can calculate:

P(X = 3) = C(10, 3) * 0.9^3 * 0.1^(10-3) = 120 * 0.9^3 * 0.1^7 = 0.0574

So, the probability of getting exactly 3 heads is 0.0574.

Thus the correct option is A) 0.0574.

Answer 2

To calculate the probability of getting exactly 3 heads when a biased coin is tossed 10 times, use the binomial probability formula with p = 0.9 and q = 0.1. The probability is 0.0574.

Step-by-step explanation:

To calculate the probability of getting exactly 3 heads when a biased coin with P(heads) = 0.9 and P(tails) = 0.1 is tossed 10 times, we can use the binomial probability formula.

The formula is:

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

Where:

• P(X = k) is the probability of getting exactly k heads
• C(n, k) is the number of ways to choose k heads from n tosses (which can be calculated using the combination formula)
• p is the probability of getting a head (0.9 in this case)
• q is the probability of getting a tail (0.1 in this case)

Using this formula, we can calculate:

P(X = 3) = C(10, 3) * 0.9^3 * 0.1^(10-3) = 120 * 0.9^3 * 0.1^7 = 0.0574

So, the probability of getting exactly 3 heads is 0.0574.