A bowl contains 10 balls, of which 4 are red and 6 are white. Balls are randomly selected with replacement from the bowl until 4 red balls have been selected. Let X be the number of white balls drawn before the fourth red ball is selected. Calculate the probability that X is 6.

The probability that X is 6 = 0.2508

Step-by-step explanation:

Probability of picking a red ball = 4 / 10 = 0.4

Probability of picking a white ball = 6 / 10 = 0.6

Let's first state that the last ball selected in this scenario will be red. This implies that we selected 6 white balls and 3 red balls in any manner before we selected the last red ball. So we need to find the probability of taking out 6 white balls and 3 red balls, and use permutation to account for the order they get drawn in:

Total Probability = Probability of 6 white balls * Probability of 3 red balls * number of ways this can happen

Probability of 6 white balls = 0.6 ^ 6

Probability of 3 red balls = 0.4 ^ 3

Number of ways this can happen (permutation with similar objects) =

Number of ways this can happen = 84

Total probability =

Total probability = 0.2508

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).