Consider a roulette wheel consisting of 38 numbers 1 through 36, 0, and double 0. if smith always bets that the outcome will be one of the numbers 1 through 12, what is the probability that smith will lose his first 5 bets; his first win will occur on his fourth bet?

0.15;

0.101

Step-by-step explanation:

Since there are 38 total options and Smith is betting on 12 possible outcomes per bet, the probability of him winning (W) and losing (L) each bet are:

The probability that Smith will lose his first 5 bets (L5) is:

The probability that his first win will occur on his fourth bet (W4) is the probability of him losing the first three bets multiplied by the probability of winning the fourth:

A. (Orthocenter) → Altitude

B. (Incenter) → Angle bisector

C. (Centroid) → Median

D. (Circumcenter) → Perpendicular bisector

Step-by-step explanation:

A. The orthocenter is the point of concurrency of the three altitudes of a triangle, therefore, the matching line with the letter A is altitude

B. The incenter is the point of concurrency of the bisectors of three interior angles of a triangle, therefore, the matching line with the letter B is angle bisector

C. The centroid is the point of concurrency of the three medians of the triangle, therefore, the matching line to the letter C is median

D. The circumcenter is the point of concurrency of the three perpendicular bisectors of the three sides of a triangle, therefore, the matching line to the letter D (which corresponds with the circumcenter) is perpendicular bisector.