Theory question 105
Triangles and Quadrilaterals(a) ABCD is a trapezium with AB parallel to DC and /AD/ = /AB/, If <BAD = 106°, find <BDC. (b) The table below shows the distribution of 20 cards labelled A – E.
Card: A, B, C, D, E
Frequency: 3, 4, 7, 5, 1
(i) If a card is selected at random from the pack, what is the probability that the card is E? (ii) If two cards are selected at random one after the other without replacement from the pack, what is the probability that one of the two cards is B?
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(a) AD = AB, so triangle ABD is isosceles: <ABD = <ADB = (180° − 106°)/2 = 37°.
AB ∥ DC, so <BDC = <ABD = 37° (alternate angles).
(b)(i) P(E) = 1/20.
(ii) 'One of the two is B' (exactly one): P(B then not B) + P(not B then B) = 4/20 × 16/19 + 16/20 × 4/19 = 64/380 + 64/380 = 128/380 = 32/95.
Without replacement the second probability uses 19 cards; remember the B card can come first or second.