33. prime numbers 34. multiples of 3 35. Construct a tree diagram showing all po

Question

33. prime numbers 34. multiples of 3 35. Construct a tree diagram showing all possible results when three fair coins are tossed. Then list the ways of getting each result. (a) at least two heads (b) more than two heads (c) no more than two heads (d) fewer than two heads 36. Extend the tree diagram of Exercise 35 for four fair coins. Then list the ways of getting each result. (a) more than three tails (b) fewer than three tails (c) at least three tails (d) no more than three tails Determine the number of triangles (of any size) in each figure 37. 38.

Explanation / Answer

36) I think below is the easiest way to represent and understand as well than tree method.

T - TAIL

H - HEAD

a) More than 3 tails also mean that 4 tails

4 Tails: TTTT

b) Fewer than 3 tails also mean that 0 or 1 or 2 tails

0 Tail: HHHH

1 Tail: THHH, HTHH, HHTH, HHHT

2 Tails: TTHH, THTH, THHT, HTTH, HTHT, HHTT

c) at least 3 tails also mean that 3 or 4 tails

3 Tails: TTTH, TTHT, THTT, HTTT

4 Tails: TTTT

d) No more than 3 tails also mean that 0 or 1 or 2 or 3 tails

0 Tail: HHHH

1 Tail: THHH, HTHH, HHTH, HHHT

2 Tails: TTHH, THTH, THHT, HTTH, HTHT, HHTT

3 Tails: TTTH, TTHT, THTT, HTTT

Thank you. Any problem in understanding please ping. Always happy to help. Thumbs up, please?

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