In hockey, Ed makes 7 goals for every 10 shots. If he takes 6 shots, what is the probability that he will make at least 5 goals?​

Explanation:

Let's consider the case where Ed makes all 6 shots. The probability of this happening is (7/10)^6 = 0.117649

Let A = 0.117649 so we can use it later.

Now consider the case where Ed makes exactly 5 shots. So he misses exactly 1 shot. Furthermore, consider the case where his first shot is a miss and the remaining 5 shots are successful.

The probability of getting the first shot a miss and the remaining 5 successful is (3/10)*(7/10)^5 = 0.050421

Note how 3/10 and 7/10 add to 1. The 3/10 is the probability of getting a miss (since he makes 7 goals for every 10 shots, he misses those 3 goals).

The value 0.050421 represents the probability for that first shot being a failed attempt while the rest are successful shots. Since there are 6 slots total, this means 6*0.050421 = 0.302526 represents the probability of missing exactly one goal and hitting the others. By this point, we aren't making the failed attempt at slot 1. It could be at any slot. For instance, the failed attempt could be at slot 4.

In other words, 0.302526 is the probability of making exactly 5 shots.

Let B = 0.302526

To recap,

These two events are mutually exclusive. They cannot happen at the same time. That allows us to add the values of A and B to get the final answer

A+B = 0.117649+0.302526 = 0.420175

Therefore, A+B = 0.420175 represents the probability of either getting all 6 shots in the goal OR getting exactly five shots in the goal.

In short, 0.420175 represents the probability of making at least 5 shots. The phrasing "at least 5" means "5 or more".

If you wanted to calculate this in one line, then you could say

(7/10)^6 + 6*(3/10)*(7/10)^5 = 0.420175

This decimal value is exact.

distance covered by pamela in 9 l of fuel = 99km

let us apply unitary method here.

distance covered by pamela in 1 l of fuel =99/9 =11 km

now let us find distance covered by pamela if she has 12 l of fuel.

distance covered in 12 l = distance covered in 1 l of fuel * 12

we know that distance covered by here in 1 l is 11 km.

so distance covered in 12 l of fuel = 11*12 = 132 km.

so a parallelogram is just like a square base times height. multiply 40 and 39 to get 1560 inches.

a triangle is base times height divided by two. so multiply 7.9 and 5 and then divide it by 2 to get 19.75inches.

the kite can be split into two separate triangles and added together to get the total area. 30 x 4 /2 which equals 60. make sure to double it for the two triangles making 120.