An urn contains one white chip and a second chip that is equally likely to be white or black. a chip is drawn at random and returned to the urn. then a second chip is drawn. what is the probability that a white appears on the second draw given that a white appeared on the first draw? (hint: let wi be the event that a white chip is selected on the ith draw, i = 1, 2. then p(w2|w1) = p(w1∩w2) p(w1) . if both chips in the urn are white, p(w1) = 1; otherwise, p(w1) = 1/2)

= 1 if both chips are white, = 1/2 otherwise

Step-by-step explanation:

represents the event that a white chip is selected on the ith draw. Then . If both chips in the urn are white, and , then . If one chip is white and the other is black, then because the event a white chip is selected on the first draw is independent from the event  a white chip is selected on the second draw, and because the chips are drawn at random.

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°