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There are 10 coins; 2 coins have heads on both sides. A coin is selected at random and tossed 5 times.

A. The probability of getting heads on all 5 tosses.
B. The probability of getting tails on at least one toss.
C. The probability of getting heads exactly 3 times.
D. The probability of getting tails on the first toss.

User Heshan
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1 Answer

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Final answer:

A. The probability of getting heads on all 5 tosses is 1024/3125. B. The probability of getting tails on at least one toss is 2101/3125.

C. The probability of getting heads exactly 3 times is 128/1250. D. The probability of getting tails on the first toss is 4/5.

Step-by-step explanation:

A. The probability of getting heads on all 5 tosses is given by the product of the probabilities of getting heads on each individual toss. Since there are 10 coins and 2 of them have heads on both sides, there are 8 coins with heads on one side and tails on the other.

Therefore, the probability of getting heads on one toss is 8/10 or 4/5. The probability of getting heads on all 5 tosses is (4/5) * (4/5) * (4/5) * (4/5) * (4/5) = 1024/3125.

B. The probability of getting tails on at least one toss is equal to 1 minus the probability of getting heads on all tosses. So, it is 1 - (1024/3125) = 2101/3125.

C. The probability of getting heads exactly 3 times can be calculated using the binomial probability formula. The formula is P(x) = (nCx) * p^x * q^(n-x), where n is the number of trials, x is the number of successful trials, p is the probability of success, and q is the probability of failure.

Step-by-step calculation:

In this case, n = 5, x = 3, p = 4/5, and q = 1 - p = 1/5. Substituting these values into the formula, we get P(3) = (5C3) * (4/5)^3 * (1/5)^(5-3) = 10 * (64/125) * (1/25).

D. The probability of getting tails on the first toss is the probability of selecting one of the 8 coins with heads on one side out of the total 10 coins. So, it is 8/10 or 4/5.

User John Mill
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