A paint-store chain produces and sells latex and semigloss paint. Based on long-range sales, the probability that a customer will purchase latex paint is 0.75. Of those that purchase latex paint, 60% also purchase rollers. But only 30% of semigloss paint buyers purchase rollers. A randomly selected buyer purchases a roller and a can of paint. What is the probability that the paint is latex?

The probability that the paint  latex = 0.857

Step-by-step explanation:

From the given information:

Let consider X to be the event that the customer has purchased the latex paint

Let consider Y to be the event that the customer has purchased semigloss paint.

Now, the probability of X i.e. P(X) = 0.75

SInce X and Y are mutually exhaustive)

P(Y) = 1 - P(X)

P(Y) = 1 - 0.75

P(Y) = 0.25

Similarly, Let Consider Z be the event that the customer has purchased a roller.

We are being told that P(Z|X) = 0.6

P(Z|Y) = 0.30

Thus, the probability that the paint  latex = 0.857

m∠cdf = 43° , m∠gdf = 114°, m∠gde = 23°, m∠edh = 23° , m∠cdh = 157°

step-by-step explanation:

since, it is given that de bisects the angle gdh ⇒ de divides the angle gdh into two equal angles.

⇒ m∠gde = m∠edh

⇒ 8·x   - 1 = 6·x + 5

⇒ x = 3

so, m∠gde = 8·x - 1 = 23°

and m∠edh = 23°

now, it is given ∠cde is an straight angle so, m∠cde = 180°

⇒ m∠cdf + m∠fdg + m∠gde = 180°

⇒ 43° + m∠fdg + 23° = 180°

⇒ m∠fdg = 114°

again, m∠cde = m∠cdh + m∠edh = 180°

m∠cdh + 23° = 180°

⇒ m∠cdh = 157°