A netball team is going to play a match on Friday and on Sunday. The probability of the team winning on Friday is 0.54 If they win on Friday, the probability of them also winning on Sunday is 0.72 If they do not win on Friday, the probability of them winning on Sunday is 0.41 (a) Complete the tree diagram

(b) Find the probability of the team winning exactly one of the two matches.

See diagram and explanations below.

Step-by-step explanation:

(a) Tree diagram: attached

(b) Probability of winning exactly one game

P(WL)+P(LW) = 0.1512 + 0.1886 = 0.3398

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12