Question

0 when coin 1 is flipped, it lands on heads with probability .4; when coin 2 is flipped, it lands on heads with probability .7. one of these coins is randomly chosen and flipped 10 times. (a) what is the probability that the coin lands on heads on exactly 7 of the 10 flips?

Answer 1

The probability that the coin lands on heads on exactly 7 of the 10 flips is approximately 0.2387.

Step-by-step explanation:

To find the probability of getting exactly 7 heads out of 10 flips, we need to consider the probability of choosing each coin and the probability of getting 7 heads for each coin.

Let's calculate the probability for each coin:

For coin 1: P(Heads) = 0.4, P(Tails) = 0.6

For coin 2: P(Heads) = 0.7, P(Tails) = 0.3

Now, we can calculate the probability of getting 7 heads for each coin:

For coin 1: P(7 Heads) = C(10, 7) * (0.4)^7 * (0.6)^3

For coin 2: P(7 Heads) = C(10, 7) * (0.7)^7 * (0.3)^3

Since we are randomly choosing one of the coins, we need to consider the probability of choosing each coin as well:

P(Coin 1) = P(Coin 2) = 0.5

Now, we can calculate the overall probability:

P(7 Heads) = P(Coin 1) * P(7 Heads for Coin 1) + P(Coin 2) * P(7 Heads for Coin 2)

P(7 Heads) = 0.5 * (C(10, 7) * (0.4)^7 * (0.6)^3) + 0.5 * (C(10, 7) * (0.7)^7 * (0.3)^3)

P(7 Heads) = 0.1176 + 0.1211

P(7 Heads) = 0.2387