suzy has 4 regular quartersand recording the results. If she does this 600 times(please read more...)?

Question

predict the number of times she will get exactly two heads.

easy points :-)

Answer 1

There are 16 combinations of heads and tails. Count the number of combos that have two heads. Multiply by 600.

TTTT
TTTH
TTHT
TTHH *
THTT
THTH *
THHT *
THHH
HTTT
HTTH *
HTHT *
HTHH
HHTT *
HHTH
HHHT
HHHH

That's 6 / 16 or 3/8

You can also use Pascal's triangle
....... 1
......1 . 1
....1 . 2 . 1
..1 . 3 . 3 . 1
1 . 4 . 6 . 4 . 1 <--- 4 (0, 1, 2, 3, 4)

For 4 coins and 2 heads, it will happens 6 times (out of 2^4 or 16). This again is 6 / 16 or 3 / 8.

Over 600 trials, you'd expect 3/8 of them to land with exactly two heads:

That's and expectation of 225 times.

Answer 2

For each trial, there are 16 possible outcomes from 2 quarters. Of those outcomes, there are (4 choose 2)=6 possible ways she can get exactly 2 heads, namely:

TTHH
THTH
THHT
HHTT
HTTH
HTHT

That means on each particular round, there is a 6/16=3/8 chance she'll get 2 heads.

If she does this 600 times, we would expect that she would have around 600*3/8 = 225 successes getting exactly 2 heads.

Answer 3

make me