To find the probability of no more than 4 launches being successful, we need to calculate the probability of 0, 1, 2, 3, or 4 launches being successful and then add them together.

Step 1: Calculate the probability of 0 successful launches.
The probability of 0 successful launches is given by (1 - success rate)^number of launches.
In this case, the success rate is 45% or 0.45, and the number of launches is 9.
So, the probability of 0 successful launches is (1 - 0.45)^9 = 0.00028243.

Step 2: Calculate the probability of 1 successful launch.
The probability of 1 successful launch is given by (success rate) * (1 - success rate)^(number of launches - 1).
In this case, the success rate is 45% or 0.45, and the number of launches is 9.
So, the probability of 1 successful launch is 9C1 * (0.45)^1 * (1 - 0.45)^(9 - 1) = 0.001989.

Step 3: Calculate the probability of 2 successful launches.
The probability of 2 successful launches is given by (success rate)^2 * (1 - success rate)^(number of launches - 2).
In this case, the success rate is 45% or 0.45, and the number of launches is 9.
So, the probability of 2 successful launches is 9C2 * (0.45)^2 * (1 - 0.45)^(9 - 2) = 0.008955.

Step 4: Calculate the probability of 3 successful launches.
The probability of 3 successful launches is given by (success rate)^3 * (1 - success rate)^(number of launches - 3).
In this case, the success rate is 45% or 0.45, and the number of launches is 9.
So, the probability of 3 successful launches is 9C3 * (0.45)^3 * (1 - 0.45)^(9 - 3) = 0.021234.

Step 5: Calculate the probability of 4 successful launches.
The probability of 4 successful launches is given by (success rate)^4 * (1 - success rate)^(number of launches - 4).
In this case, the success rate is 45% or 0.45, and the number of launches is 9.
So, the probability of 4 successful launches is 9C4 * (0.45)^4 * (1 - 0.45)^(9 - 4) = 0.034902.

Step 6: Add up the probabilities from steps 1 to 4.
The probability of no more than 4 launches being successful is the sum of the probabilities calculated in steps 1 to 4.
So, the probability is 0.00028243 + 0.001989 + 0.008955 + 0.021234 + 0.034902 = 0.06736243.

Therefore, the probability of no more than 4 launches being successful is approximately 0.0674 or 6.74%.

Question

To find the probability of no more than 4 launches being successful, we need to calculate the probability of 0, 1, 2, 3, or 4 launches being successful and then add them together.

Step 1: Calculate the probability of 0 successful launches.
The probability of 0 successful launches is given by (1 - success rate)^number of launches.
In this case, the success rate is 45% or 0.45, and the number of launches is 9.
So, the probability of 0 successful launches is (1 - 0.45)^9 = 0.00028243.

Step 2: Calculate the probability of 1 successful launch.
The probability of 1 successful launch is given by (success rate) * (1 - success rate)^(number of launches - 1).
In this case, the success rate is 45% or 0.45, and the number of launches is 9.
So, the probability of 1 successful launch is 9C1 * (0.45)^1 * (1 - 0.45)^(9 - 1) = 0.001989.

Step 3: Calculate the probability of 2 successful launches.
The probability of 2 successful launches is given by (success rate)^2 * (1 - success rate)^(number of launches - 2).
In this case, the success rate is 45% or 0.45, and the number of launches is 9.
So, the probability of 2 successful launches is 9C2 * (0.45)^2 * (1 - 0.45)^(9 - 2) = 0.008955.

Step 4: Calculate the probability of 3 successful launches.
The probability of 3 successful launches is given by (success rate)^3 * (1 - success rate)^(number of launches - 3).
In this case, the success rate is 45% or 0.45, and the number of launches is 9.
So, the probability of 3 successful launches is 9C3 * (0.45)^3 * (1 - 0.45)^(9 - 3) = 0.021234.

Step 5: Calculate the probability of 4 successful launches.
The probability of 4 successful launches is given by (success rate)^4 * (1 - success rate)^(number of launches - 4).
In this case, the success rate is 45% or 0.45, and the number of launches is 9.
So, the probability of 4 successful launches is 9C4 * (0.45)^4 * (1 - 0.45)^(9 - 4) = 0.034902.

Step 6: Add up the probabilities from steps 1 to 4.
The probability of no more than 4 launches being successful is the sum of the probabilities calculated in steps 1 to 4.
So, the probability is 0.00028243 + 0.001989 + 0.008955 + 0.021234 + 0.034902 = 0.06736243.

Therefore, the probability of no more than 4 launches being successful is approximately 0.0674 or 6.74%.

Knowee AI · Accepted Answer